A PHOTOCELL EXPERIMENT FOR
SECONDARY SCHOOL PHYSICS
by
B.Sc,
RONALD D. MACQUEEN
U n i v e r s i t y of B r i t i s h Columbia,
1960
A THESIS SUBMITTED IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR THE DEGREE
OF MASTER OF ARTS
i n the
Faculty
of
Education
We accept t h i s t h e s i s as conforming
to the r e q u i r e d standard
THE UNIVERSITY OF BRITISH COLUMBIA
April,
1966
In p r e s e n t i n g t h i s t h e s i s
the requirements
in p a r t i a l
fulfilment
of
f o r an advanced degree at the U n i v e r s i t y
of
B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make i t
freely
available for
per-
r e f e r e n c e and s t u d y .
I f u r t h e r agree t h a t
mission for extensive copying of t h i s
thesis for
scholarly
purposes may be g r a n t e d by the Head o f my Department o r by
h i s representatives..
c a t i o n of t h i s
It
i s understood t h a t c o p y i n g o r
thesis for financial
w i t h o u t my w r i t t e n p e r m i s s i o n .
Department of
OC4T"'OtJ
The U n i v e r s i t y o f B r i t i s h Columbia
Vancouver 8, Canada
Date
/IP&JL
,
publi-
g a i n s h a l l not be a l l o w e d
ABSTRACT
There was r e c e n t l y i n t r o d u c e d i n t o t h e secondary s c h o o l s
of
the
of
B r i t i s h Columbia a c o u r s e i n p h y s i c s based p r i m a r i l y upon
work of t h e P h y s i c a l S c i e n c e Study Committee.
t h e c o u r s e a study i s made o f a t o m i c p h y s i c s .
At t h e end
A fundamental
concept i n v o l v e d i n t h e study o f a t o m i c p h y s i c s i s t h a t o f t h e
quantum o f l i g h t energy.
A p h o t o c e l l experiment s u i t a b l e f o r
use i n secondary s c h o o l s has been developed which i s i n t e n d e d
to
h e l p t h e s t u d e n t t o come t o major c o n c l u s i o n s r e g a r d i n g t h e
p h o t o e l e c t r i c e f f e c t and t h e n a t u r e o f l i g h t .
In d e v e l o p i n g t h i s experiment i n v e s t i g a t i o n s were made t o
d e t e r m i n e t h e s u i t a b i l i t y o f a v a i l a b l e a p p a r a t u s and methods.
Among t h e a s p e c t s i n v e s t i g a t e d were p h o t o c e l l s , l i g h t s o u r c e s ,
f i l t e r s , methods o f measuring s m a l l c u r r e n t s , and methods o f
i n v e s t i g a t i n g the p h o t o e l e c t r i c e f f e c t .
The experiment which
e v o l v e d was then performed under c o n d i t i o n s more s u i t a b l e than
e x i s t i n secondary s c h o o l s .
The r e s u l t s o f t h e experiment
agreed w i t h t h e major p o i n t s o f t h e t h e o r y and y i e l d e d a v a l u e
for
P l a n c k ' s c o n s t a n t w i t h i n t e n p e r cent o f a c c e p t e d v a l u e .
I t was c o n c l u d e d t h a t a p h o t o c e l l experiment can be p e r -
formed i n secondary s c h o o l s which w i l l y i e l d r e s u l t s which
agree w i t h t h e t h e o r y .
TABLE OF CONTENTS
PAGE
CHAPTER 1 -
INTRODUCTION
1
1.1
The Problem
1
1.2
H i s t o r y of the P h o t o e l e c t r i c
1.3
Review of the L i t e r a t u r e
1.4
C r i t e r i a to be Met by the Experiment
Effect
. . .
3
8
.
.
CHAPTER 2 - THEORY
CHAPTER 3 - EXPERIMENTAL
11
13
INVESTIGATIONS AND RESULTS
25
3.1
Photocells
25
3.2
F i l t e r s and L i g h t Sources
30
3.3
Method
35
3.4
Methods of Measuring Small C u r r e n t s
3.5
Summary
. . .
40
43
CHAPTER 4 - A PHOTOCELL DETERMINATION OF PLANCK'S
CONSTANT
45
4.1
Method
45
4.2
Results
47
4.3
D i s c u s s i o n of R e s u l t s
52
4.4
Conclusions
54
CHAPTER 5 - A PHOTOCELL EXPERIMENT FOR SECONDARY
SCHOOL PHYSICS
56
5.1
Introduction
56
5.2
The Experiment
57
PAGE
BIBLIOGRAPHY
APPENDIX A - A d d i t i o n a l data taken with
lens and n e u t r a l f i l t e r
61
glass
APPENDIX B - L i s t of s p e c i a l apparatus and
catalogue numbers
64
67
LIST OF TABLES
PAGE
3.1
Maximum p o t e n t i a l d i f f e r e n c e a c r o s s
c h a r g e d with a Leybold p h o t o c e l l
capacitors
39
LIST OF
ILLUSTRATIONS
PAGE
2.1
2.2
F e r n u - D i r a c d i s t r i b u t i o n of k i n e t i c e n e r g i e s
of f r e e e l e c t r o n s i n a metal
17
Contact p o t e n t i a l d i f f e r e n c e
flow between two metals
19
due
to
electron
2.3
Photocurrent as a f u n c t i o n of a p p l i e d
difference
2.4
C h a r a c t e r i s t i c s of a p h o t o c e l l with r e v e r s e
current
23
3.1
C h a r a c t e r i s t i c s of o l d Leybold p h o t o c e l l
27
3.2
C h a r a c t e r i s t i c s of new
Leybold p h o t o c e l l s
. . . .
27
3.3
C h a r a c t e r i s t i c s of 929
and
. . . .
29
3.4
C h a r a c t e r i s t i c s of 5581
3.5
C h a r a c t e r i s t i c s of 926
3.6
C h a r a c t e r i s t i c s of Leybold p h o t o c e l l
37
3.7
Twin t r i o d e b r i d g e c i r c u i t
41
3.8
Transistor
c i r c u i t to measure s m a l l c u r r e n t s
4.1a
Electrical
circuit
4.1b
O p t i c a l system
4.1c
Apparatus f o r p h o t o c e l l
4.2
Characteristics for u l t r a - v i o l e t
4.3
C h a r a c t e r i s t i c s f o r blue l i g h t
49
4.4
C h a r a c t e r i s t i c s f o r green l i g h t
49
4.5
C h a r a c t e r i s t i c s f o r yellow l i g h t
50
4.6
Relationship
frequency
5.1
Circuit
1P39
potential
photocells
photocell
20
29
photocell
31
„ . .
42
46
46
experiment
light
between s t o p p i n g p o t e n t i a l
f o r p h o t o c e l l experiment
48
48
and
50
58
ACKNOWLEDGEMENT
I wish t o express my s i n c e r e s t thanks
t o Dr. D. L. L i v e s e y
of the P h y s i c s Department f o r s u g g e s t i n g the t o p i c f o r t h i s
t h e s i s and f o r h i s p a t i e n t guidance
out.
and encouragement
through-
I am a l s o indebted to Dr. R. E. Burgess of the P h y s i c s
Department f o r h i s time spent i n d i s c u s s i o n and many h e l p f u l
suggestions.
Thanks a r e a l s o due t o Dr. R. V. Boughton of the F a c u l t y
of Education f o r making the f a c i l i t i e s of the Science Department
a v a i l a b l e , t o Mrs. J . Woodrow of the F a c u l t y of Education f o r
her c a r e f u l p r o o f - r e a d i n g and many suggestions r e g a r d i n g the
w r i t i n g of the t h e s i s , and t o Mr. G. R. Haney f o r s u p p l y i n g the
transistor circuit
and t e c h n i c a l a d v i c e .
I g r a t e f u l l y acknowledge the r e c e i p t of a s c h o l a r s h i p
from the U n i v e r s i t y to enable me t o c a r r y on a summer of
research.
CHAPTER 1.
1.1
INTRODUCTION
The Problem.
Recently
there was i n t r o d u c e d i n t o the secondary
schools
of B r i t i s h Columbia a course i n p h y s i c s based p r i m a r i l y upon the
work of the P h y s i c a l Science
years
Study Committee
work i n t h i s course the student
(PSSC).
i s given the
In two
opportunity
to study the behaviour of matter and energy and to d i s c o v e r
of the fundamental concepts which have been developed
t h i s behaviour.
At the c o n c l u s i o n of
some
concerning
the course the student
i n t r o d u c e d to the s t u i y of atomic p h y s i c s ,
is
g i v i n g him the
o p p o r t u n i t y to begin to understand the r e l a t i o n s h i p among some
of the t o p i c s
studied e a r l i e r .
Fundamental to an understanding
of atomic phenomena i s the concept of a quantum of energy.
At
present there i s no method c o n s i s t e n t w i t h the p h i l o s o p h y of
the course to develop t h i s
concept.
The p h i l o s o p h y upon which the present course i s based
p r i m a r i l y an experimental
the development
used i n p h y s i c s ,
one.
i n the student
and to
Among i t s most important
of an a p p r e c i a t i o n
t h i s end the student
p h y s i c s r a t h e r than watch i t
b e i n g done.
is
aims
f o r the
is
methods
i s r e q u i r e d to do
An e x p r e s s i o n
p h i l o s o p h y i s to be found i n the i n t r o d u c t i o n to the
guide p u b l i s h e d by the B r i t i s h Columbia Department
of
of
this
curriculum
Education.
T r a d i t i o n a l p h y s i c s courses g e n e r a l l y have been c o n cerned with d e s c r i p t i o n and i n f o r m a t i o n .
This information
has been at the expense of l e a r n i n g processes and methods.
The tremendous expansion of knowledge i n t h i s f i e l d has now
made i t i m p o s s i b l e to give a l l the f a c t u a l d e t a i l .
It has
2
been c o n s i d e r e d d e s i r a b l e to c o n c e n t r a t e the e f f o r t s of
students on p r i n c i p l e s and methods.
1
In keeping with t h i s p h i l o s o p h y , each step i n the development of a t o p i c must be a r r i v e d at by experiment,
the students themselves.
p r e f e r a b l y by
At no p o i n t can the teacher f a l l
back
upon dogmatism which i s t o be b l i n d l y accepted by the students
as t r u t h .
However, no experiment
time which can be used
to develop
i s a v a i l a b l e a t the present
the concepts of a quantum of
energy.
The
two year course i s intended t o present to the student
the t o t a l p i c t u r e of p h y s i c s , so that even the student who w i l l
never again study p h y s i c s as a d i s c i p l i n e w i l l have done a comprehensive p i e c e of work i n p h y s i c s .
s i o n of atomic p h y s i c s cannot
important
atomic
For t h i s reason the i n c l u -
be avoided.
Many of the most
advances of t h i s century have been i n the f i e l d of
p h y s i c s and i n t h i s r e s p e c t atomic p h y s i c s i s no longer a
modern and s p e c i a l i z e d study.
It i s very much a p a r t of everyday
l i v i n g and so has an important
place i n general education.
In d e v e l o p i n g the u n i t on atomic
that the concept
p h y s i c s i t was decided
of the photon i s b a s i c .
In view of the e x p e r i -
mental nature of the course, there i s a need f o r an
or
s e r i e s of experiments
which can be performed
experiment
e i t h e r by the
students or by the teacher to develop an understanding
concept.
of t h i s
Since the d i s c o v e r y of the nature of the p h o t o e l e c t r i c
1 B r i t i s h Columbia, Department of E d u c a t i o n , D i v i s i o n of
C u r r i c u l u m , Senior Secondary School Science, P h y s i c s 12, 1965,
p. 7.
•
!
o
e f f e c t was l a r g e l y r e s p o n s i b l e f o r the acceptance of the e x i s t ence of quanta of energy, an experiment
electric
effect
i n v o l v i n g the photo-
i s thought t o be a most u s e f u l way to develop the
concept of the quantum of energy.
It i s the purpose of t h i s t h e s i s t o develop an experiment
or
s e r i e s of experiments f o r secondary s c h o o l p h y s i c s based
upon the p h o t o e l e c t r i c e f f e c t .
The purpose of the experiments
i s t o develop the concept of the quantum of energy and t o measure
Planck's c o n s t a n t .
1.2
H i s t o r y of the P h o t o e l e c t r i c
In
1887, w h i l e i n the process of doing r e s e a r c h on the r e s o n 2
ance of e l e c t r i c a l c i r c u i t s , H e r t z
effect.
Effect.
d i s c o v e r e d the p h o t o e l e c t r i c
He observed that the l e n g t h of a spark which could be
induced i n a secondary c i r c u i t was much reduced i f the spark gap
was s h i e l d e d from the l i g h t of the spark i n the primary c i r c u i t .
He went on t o determine that the e f f e c t was due e n t i r e l y
to the
i l l u m i n a t i o n of the e l e c t r o d e s , that only the u l t r a - v i o l e t
p o r t i o n of the l i g h t was e f f e c t i v e , and that the spark was longest
when the n e g a t i v e e l e c t r o d e was b e i n g i l l u m i n a t e d .
3
i n v e s t i g a t i o n s Hallwachs
In f u r t h e r
showed that a p o l i s h e d z i n c p l a t e
connected t o an e l e c t r o s c o p e would r e t a i n a p o s i t i v e charge w h i l e
being i l l u m i n a t e d by l i g h t
from a carbon a r c , but would l o s e a
2 A. L: Hughes and L. A. DuBridge, P h o t o e l e c t r i c Phenomena,
New York, McGraw-Hill, 1932, p. 3.
3 I b i d . , p. 3
4
n e g a t i v e charge when i l l u m i n a t e d .
due
This e f f e c t could only
t o l o s s of n e g a t i v e e l e c t r i c i t y , f o r any
be
gain i n p o s i t i v e
e l e c t r i c i t y would have to r e s u l t from p o s i t i v e e l e c t r i c i t y
a r r i v i n g w i t h the l i g h t .
experiment.
Such a t h e o r y cannot be supported
I t has r e c e n t l y been shown t h a t an
by
electroscope
can a l s o be charged by i l l u m i n a t i n g i t under the r i g h t c o n d i t i o n s
5
By 1899
both Lenard
6
and
Thomson
had shown t h a t the nega-
t i v e l y charged p a r t i c l e s i n v o l v e d were i n d e n t i c a l t o
found i n cathode r a y s and
thus were e l e c t r o n s .
those
7
Lenard
also
showed t h a t the maximum k i n e t i c e n e r g i e s of the r e l e a s e d e l e c t r o n s were independent of the i n t e n s i t y of the l i g h t used but
t h a t the number of e l e c t r o n s r e l e a s e d was
to the l i g h t
The
directly proportional
intensity.
experimental
the p h o t o e l e c t r o n s
f a c t t h a t the maximum k i n e t i c e n e r g i e s
are independent of the i n t e n s i t y of the
c o n t r a d i c t s what one would expect from a c o n s i d e r a t i o n of
c l a s s i c a l wave t h e o r y of l i g h t .
According
of
light
the
to t h i s theory,
an
i n c r e a s e i n l i g h t i n t e n s i t y i s due
t o an i n c r e a s e i n the
tude of the e l e c t r o m a g n e t i c
An e l e c t r o n c l o s e t o the s u r -
wave.
ampli-
4 J . E. M i l l e r , A. ft. Reed, and D. P. M i l l e r , " P h o t o e l e c t r i c
Charging of an E l e c t r o s c o p e " , American J o u r n a l of P h y s i c s , v o l .
34 (1966), p. 172.
5 P. L e n a r d , "The P r o d u c t i o n of Cathode Rays by U l t r a - v i o l e t
L i g h t " , Annalen der P h y s i k , v o l . 2 (1900), pp. 359-375.
6 J . J . Thomson, "On the Masses of Ions a t Low P r e s s u r e s " ,
P h i l o s o p h i c a l Magazine, s e r i e s 5, v o l . 48 (1899), pp. 547 - 567.
7 Hughes and D u B r i d g e , P h o t o e l e c t r i c Phenomena, p.
4.
c
5
f a c e of a metal would experience a much g r e a t e r f o r c e due t o the
large e l e c t r i c
field
field
than i t would due to the s m a l l e r e l e c t r i c
of lower i n t e n s i t y
light.
T h i s g r e a t e r f o r c e would be
expected to g i v e the e l e c t r o n s i t p u l l s from the metal g r e a t e r
a c c e l e r a t i o n and g r e a t e r k i n e t i c energy
than the f o r c e due to
the l e s s i n t e n s e l i g h t .
There i s a f u r t h e r c o n t r a d i c t i o n as w e l l .
A c c o r d i n g t o the
wave model of l i g h t an atom would r e q u i r e a time of order of
hours to absorb enough energy
to
from an e l e c t r o m a g n e t i c wave t r a i n
e j e c t an e l e c t r o n with the k i n e t i c energy
observed.
It has
been shown that the time l a p s e between i l l u m i n a t i o n and the onset
of
-9
p h o t o e l e c t r i c c u r r e n t i s not more than 3 x 10"
8
seconds.
9
In
to
1905
Einstein
p u b l i s h e d a h y p o t h e s i s which enabled
p r e d i c t the maximum k i n e t i c energy
that an e l e c t r o n c o u l d have
when emitted from an i l l u m i n a t e d m e t a l l i c s u r f a c e .
Einstein
p o s t u l a t e d the e x i s t e n c e of a l i g h t c o r p u s c l e or photon
energy of magnitude h f , where f was
The constant,h,was
him
with
the frequency of the
-34
Planck's c o n s t a n t , 6.63
x 10
light.
joule-second,
which had r e c e n t l y been i n t r o d u c e d by Planck i n h i s quantum
theory.
to
to
E i n s x e i n assumed that t h i s photon gave a l l of i t s energy
one e l e c t r o n .
If t h i s e l e c t r o n had to do an amount of work,w,
escape from the metal, then i t s k i n e t i c e n e r g y , K , a f t e r l e a v i n g
8 G. P. Barnwell and J . J . L i v i n g o o d , Experimental
P h y s i c s , New York, McGraw-Bill, 1933, p. 214.
Atomic
9 A. E i n s t e i n , " L i g h t Generation and L i g h t A b s o r p t i o n , "
Annalen der Physik, v o l . 20 (1906), pp. 199 - 206.
6
the s u r f a c e would be given by
K = hf - w
(1.1)
An e x p l a n a t i o n of the phenomena observed by Lenard i s
r e a d i l y a r r i v e d at u s i n g the above model.
light
intensity
In t h i s case i n c r e a s e d
i s due to an i n c r e a s e d number of photons.
each photon has energy of magnitude h f , the r e s u l t
Since
i s more e l e c -
t r o n s emitted and thus l a r g e r p h o t o c u r r e n t , but no i n c r e a s e i n
the k i n e t i c e n e r g i e s of these e l e c t r o n s .
of
the photon
Since a l l of the energy
i s given to an e l e c t r o n at once, the time l a p s e
r e q u i r e d by the wave model i s no longer necessary.
The E i n s t e i n h y p o t h e s i s had s t i l l
to be v e r i f i e d
a l l y and d u r i n g the next ten years much work was
the r e s u l t s were s t i l l
not c l e a r , however.
experiment-
done.
By
1915
Slopes f o r the
k i n e t i c energy - frequency graphs v a r i e d by as much as s i x t y
cent and i t was
not even c l e a r that the r e l a t i o n s h i p between
10
k i n e t i c energy and frequency was
Ladenburg
to
per
linear.
concluded that the energy was
In 1907,
directly
f o r example,
proportional
the square of the frequency, but J o f f e l a t e r worked over
Ladenburg's data and showed that they j u s t as w e l l f i t a l i n e a r
r e l a t i o n s h i p between energy and frequency because
of the s m a l l
range of f r e q u e n c i e s used and the l a r g e u n c e r t a i n t i e s
involved.
10 R. A. M i l l i k a n , "A D i r e c t P h o t o e l e c t r i c Determination of
Planck's 'h', The P h y s i c a l Review, s e r i e s 2, v o l . 7 (1916),
p. 357.
M
11 I b i d . , p.
357.
1 1
Richardson
1912
and
and
concluded
Corapton
that the maximum e l e c t r o n energy was
f u n c t i o n of the frequency
Hughes ^ found
1
l i n e a r , but
s h i p was
d i d much more r e l i a b l e work i n
of the l i g h t .
relationship
that the s l o p e of the graph of t h i s
c o n s i s t e n t l y lower than expected,
a l i of the energy of the photon was
Millikan later critized
was
relation-
c o n c l u d i n g that not
t r a n s f e r r e d to the e l e c t r o n s .
t h i s work on the grounds that only
p o i n t s on the graph were l o c a t e d and
j u s t i f y any
linear
About the same time
that the energy - frequency
found
a
three
that three p o i n t s cannot
c o n c l u s i o n s about the shape of the graph.
14
It was
left
to M i l l i k a n
to a high degree of accuracy.
developed
to check E i n s t e i n ' s hypothesis
In 1915
a l a r g e g l a s s tube
was
which would remove i n a vacuum a l l of the s u r f a c e
f i l m s from the metal being s t u d i e d .
to measure s i m u l t a n e o u s l y
A method was
the magnitude of the
the e n e r g i e s of the p h o t o e l e c t r o n s , and
developed
photocurrent,
the contact
d i f f e r e n c e s between the s u r f a c e s i n v o l v e d .
potential
Measurements were
made over as great a range of f r e q u e n c i e s of l i g h t as p o s s i b l e .
A f t e r t a k i n g many p r e c a u t i o n s to a v o i d the e r r o r s and
uncertain-
t i e s encountered i n the work of most of the other i n v e s t i g a t i o n s
12 0. W. Richardson and K. T. Compton, "The P h o t o e l e c t r i c
E f f e c t , " P h i l o s o p h i c a l Magazine, s e r i e s 6, v o l . 24 (1912),
pp. 575 - 594.
13 A. L. Hughes, "On the Emission V e l o c i t i e s of P h o t o - E l e c t r o n s ,
P h i l o s o p h i c a l T r a n s a c t i o n s of the Royal S o c i e t y of London,
s e r i e s A, v o l . 212 (1913), pp. 205 - 226.
14 M i l l i k a n ,
"Planck's
'h'," pp.
355
-
388.
8
to that time ,MiIlikan concluded that a l i n e a r r e l a t i o n s h i p d i d
e x i s t between maximum e l e c t r o n e n e r g i e s and the frequency o f the
light.
The s l o p e of the energy
- frequency graph was found t o
agree with the known and accepted values of h.
1.3
Review of the L i t e r a t u r e .
A review o f the p h y s i c s a b s t r a c t s from 1910 to 1964 r e v e a l s
t h a t , although much work has been done i n v e s t i g a t i n g the photoe l e c t r i c e f f e c t and d e v e l o p i n g p h o t o e l e c t r i c c e l l s ,
have been made and r e p o r t e d to develop a p h o t o c e l l
s u i t a b l e f o r use i n secondary
The e a r l i e s t
few attempts
experiment
school physics.
p h o t o c e l l demonstration f o r secondary s c h o o l s
15
r e p o r t e d was due to Suhrmann.
He used a p h o t o c e l l
irradiated
s u c c e s s i v e l y by the blue and yellow l i n e s of the mercury
Using a simple potentiometer c i r c u i t
the maximum p o t e n t i a l
erence developed by the c e l l was measured i n each case.
constant was then c a l c u l a t e d
spectrum.
diff-
Planck's
from
(1.2)
where e i s the charge on an e l e c t r o n , V i s the p o t e n t i a l
erence, and f the frequency of the l i g h t
diff-
used.
15 R. Suhrmann, "Determination o f Planck's Constant as a
Q u a n t i t a t i v e L e c t u r e Experiment," P h y s i k a l i s c h e Z e i t s c h r i f t ,
v o l . 33 (1932), p. 579.
9
A somewhat d i f f e r e n t arrangement was used by Aussenegg
to measure the maximum p o t e n t i a l d i f f e r e n c e developed
photocell.
He connected
the c a p a c i t o r by i l l u m i n a t -
the p h o t o c e l l w i t h l i g h t of known frequency.
charge Q accumulated
by the
a c a p a c i t o r between the e m i t t e r and
c o l l e c t o r of a p h o t o c e l l and charged
ing
16
The maximum
on the c a p a c i t o r was measured f o r each
frequency by d i s c h a r g i n g i t through a b a l l i s t i c
galvanometer.
The p o t e n t i a l d i f f e r e n c e V a c r o s s the c a p a c i t o r was found
from
Q
V =
(1.3)
C
where C was the c a p a c i t a n c e .
Since V was a l s o the p o t e n t i a l
d i f f e r e n c e a c r o s s the p h o t o c e l l , h was c a l c u l a t e d from equation
1.2.
17
S t i l l another
v a r i a t i o n was r e p o r t e d by Davis.
A chopper
c o n s i s t i n g of a r o t a t i n g d i s c with e q u a l l y spaced h o l e s around
i t s perimeter was p l a c e d between the l i g h t
cell.
source and the photo-
Since the l i g h t was passed at i n t e r v a l s , the photocurrent
produced
was an a l t e r n a t i n g one.
T h i s was a m p l i f i e d u s i n g an
audio a m p l i f i e r and d e t e c t e d with earphones.
A stopping p o t e n t i a l
d i f f e r e n c e was a p p l i e d t o the p h o t o c e l l , making the c o l l e c t o r
16 F. Aussenegg, "A Simple Method f o r the Determination of
Planck's Constant," Acta P h y s i c a A u s t r i a c a , v o l . 14 (1961),
pp. 440 - 444.
17 S. P. D a v i s , " P h o t o e l e c t r i c E f f e c t Experiment,"
J o u r n a l of P h y s i c s , v o l . 29 (1961), pp. 706 - 707.
American
10
n e g a t i v e with r e s p e c t t o the e m i t t e r .
The minimum negative
p o t e n t i a l d i f f e r e n c e f o r which a s i g n a l was a u d i b l e was used as
a measure of the maximum k i n e t i c energy of the e l e c t r o n s .
Planck's constant was then c a l c u l a t e d u s i n g equation 1.2.
An e v a l u a t i o n of two commercial systems f o r the measurement
of
Planck's constant which a r e s u i t a b l e f o r use i n secondary
18
s c h o o l s has been made by Hansen and C l o t f e l t e r .
The f i r s t
of
these i s the system manufactured by E. Leybold's
Nachfolger
of
West Germany c o n s i s t i n g of a mercury vapour lamp, d i r e c t
v i s i o n prism, p h o t o c e l l measuring a m p l i f i e r , and a p p r o p r i a t e
l e n s e s , s l i t s and h o l d e r s .
I t was found
that a p p r e c i a b l e c o l l e c t -
or c u r r e n t s due t o p h o t o e l e c t r o n s being emitted from the c o l l e c t or and going t o the e m i t t e r made the d e t e r m i n a t i o n of the a p p l i e d
p o t e n t i a l d i f f e r e n c e necessary
zero very u n c e r t a i n .
F u r t h e r problems were encountered
the c o l l e c t o r was heated
with the equipment.
to reduce the photocurrent t o
as i n s t r u c t e d
when
i n the l i t e r a t u r e s u p p l i e d
The p o t e n t i a l d i f f e r e n c e a c r o s s the c e l l
was
found
t o vary with the l e n g t h of time elapsed between heat-
ing
the c o l l e c t o r and making the measurements.
These problems
were l a r g e l y o f f s e t by the f a c t that the apparatus
i s clearly
v i s i b l e to the s t u d e n t s .
The experimental arrangement has s i g n i f i c a n t i n s t r u c t i o n a l value.
Nearly a l l p a r t s a r e c l e a r l y v i s i b l e and a r e
18 R. J . Hansen and B. E. C l o t f e l t e r , " E v a l u a t i o n of Commerc i a l Apparatus f o r Measuring h/e," American J o u r n a l of P h y s i c s ,
v o l . 34 (1966), pp. 75 - 78.
11
very a c c e s s i b l e . S e l e c t i n g the d e s i r e d l i n e by adjustment
of the d i r e c t v i s i o n p r i s m , v a r y i n g the r e t a r d i n g p o t e n t i a l ,
and r e a d i n g the c u r r e n t a r e a l l o p e r a t i o n s which h e l p the
s t u d e n t t o u n d e r s t a n d the method c l e a r l y . A l t h o u g h p r e c i s e
r e s u l t s cannot be r e l i a b l y o b t a i n e d w i t h the equipment,
the experiment d e f i n i t e l y has e d u c a t i o n a l v a l u e . ^
The second system i s manufactured by Madison
of Madison, New
Jersey.
In t h i s arrangement
Associates
the p h o t o c e l l i s
housed i n a c a s i n g w i t h t e n f i l t e r s , a f i l t e r magazine, and a
p o w e r f u l mercury lamp.
The p h o t o c e l l i s used t o charge a
c a p a c i t o r , i t s p o t e n t i a l d i f f e r e n c e b e i n g measured w i t h an
electrometer-type
d i r e c t c u r r e n t vacuum-tube v o l t m e t e r .
i s compact, easy t o u s e , and y i e l d s a c c u r a t e r e s u l t s .
d i s a d v a n t a g e i s t h a t the student
The u n i t
I t s chief
cannot see i n s i d e the c a s i n g
and so does not have an o p p o r t u n i t y t o f u l l y u n d e r s t a n d what he
i s doing.
The t o t a l c o s t of the u n i t i s i n the neighbourhood of
$750.
I t i s s i g n i f i c a n t t h a t i n n e i t h e r case was any mention made
of v a r y i n g the i n t e n s i t y of the l i g h t a l t h o u g h
important
1.4
t h i s i s a very
a s p e c t of the e x p e r i m e n t .
C r i t e r i a t o be Met by the E x p e r i m e n t .
Two b a s i c c r i t e r i a must be met by a p h o t o c e l l experiment
for
secondary s c h o o l s .
The experiment must c l e a r l y
demonstrate
the major phenomena i n v o l v e d and do so i n a manner r e a d i l y understood by secondary s c h o o l
19 I b i d . , p. 77.
students.
With r e g a r d t o t h e f i r s t c r i t e r i o n , two e x p e r i m e n t a l
f a c t s s h o u l d become c l e a r as t h e r e s u l t s o f t h e experiment a r e
analyzed.
The maximum k i n e t i c energy o f an e l e c t r o n
ejected
from t h e i l l u m i n a t e d s u r f a c e o f a m e t a l i s a l i n e a r f u n c t i o n o f
the frequency
of the l i g h t .
T h i s energy i s i n no way a f f e c t e d
by t h e i n t e n s i t y o f t h e l i g h t , however.
methods o f d e m o n s t r a t i n g
Most o f t h e a v a i l a b l e
t h e p h o t o e l e c t r i c e f f e c t do not emph-
a s i z e t h e e f f e c t o f t h e changing
l i g h t i n t e n s i t y , but t h e whole
quantum approach t o t h e p h o t o e l e c t r i c i s meaningless
unless
this
independence o f e l e c t r o n e n e r g i e s from t h e i n t e n s i t y o f l i g h t
is
established.
The method used t o a r r i v e a t t h e above c o n c l u s i o n s must be
r e a d i l y understood
by t h e s t u d e n t s p e r f o r m i n g t h e experiment.
I n s t r u m e n t a t i o n must be kept as s i m p l e as p o s s i b l e and data
s h o u l d be such t h a t i t can be a n a l y z e d u s i n g methods f a m i l i a r
to the student.
The s t u d e n t s h o u l d then be f r e e t o c o n c e n t r a t e
upon t h e s i g n i f i c a n c e of t h e r e s u l t s he has o b t a i n e d .
CHAPTER 2.
Although
to
THEORY
from equation 1.1
be a r e l a t i v e l y
the p h o t o e l e c t r i c e f f e c t
simple phenomenon t o i n v e s t i g a t e , many
f a c t o r s enter to make the data gathered i n an experiment
cult
to i n t e r p r e t .
appears
diffi-
C h i e f among these f a c t o r s are contact poten-
t i a l d i f f e r e n c e s between e m i t t e r and c o l l e c t o r , and c u r r e n t s i n
a d i r e c t i o n o p p o s i t e to that of the p h o t o c u r r e n t .
be found to measure the k i n e t i c energy
A method must
of p h o t o e l e c t r o n s and
frequency of the l i g h t must be c l e a r l y d e f i n e d .
Only
after
c a r e f u l c o n s i d e r a t i o n of these f a c t o r s can the data be used
a r r i v e at c o n c l u s i o n s c o n s i s t e n t with equation
From equation 1.1
energy
to
1.1.
i t can be seen that a graph of the k i n e t i c
of p h o t o e l e c t r o n s as a f u n c t i o n of l i g h t
straight
the
l i n e with s l o p e h.
Equation 1.1 was
frequency i s a
written after a
c o n s i d e r a t i o n of only one photon and one e l e c t r o n , however.
the l i g h t
has energy
If
i s monochromatic i t can be assumed that each photon
hf.
These photons a f f e c t the f r e e e l e c t r o n s w i t h i n
1
a very t h i n l a y e r on the i l l u m i n a t e d s u r f a c e ,
and these e l e c t r o n s
have a d i s t r i b u t i o n of k i n e t i c e n e r g i e s a f t e r e s c a p i n g the
s u r f a c e , depending
upon the amounts of energy
the e l e c t r o n s from the metal.
assume that the energy
equation 1.1
electrons.
expended i n removing
Since there i s no reason to
expended i s the same f o r each
electron,
must be w r i t t e n f o r the more g e n e r a l case of many
If the assumption
i s made that there i s a minimum
amount of work necessary to remove an e l e c t r o n from the metal,
New
1 A. L. Hughes and L. A. DuBridge,
York, McGraw-Hill, 1932, p. 9.
P h o t o e l e c t r i c Phenomena,
14
the work f u n c t i o n p, then there
the p h o t o e l e c t r o n s ,K ,defined
M
1.1
may
be w r i t t e n i n the
K
M
i s a maximum k i n e t i c energy of
by equation 1.1.
Thus, equation
form
- hf - p
(2.1)
2
Various
methods have been t r i e d to measure K.,.
M
measured the v e l o c i t i e s of the p h o t o e l e c t r o n s
ic deflections.
If a magnetic f i e l d
Ramsauer
by means of magnet-
B i s a p p l i e d at r i g h t angles
to the d i r e c t i o n of motion of a p h o t o e l e c t r o n ,
the
electron
e x p e r i e n c e s a f o r c e at r i g h t angles to both of magnitude
where v i s the v e l o c i t y of the e l e c t r o n .
t u r n i n a c i r c l e of r a d i u s r d e f i n e d
r =
The
Bev
electron w i l l
by
mv
—
Be
(2.2)
where m i s the mass of the e l e c t r o n .
The
v e l o c i t y and
hence
k i n e t i c energy of the e l e c t r o n s can be determined by measuring
r.
Another method i n v o l v e s the use of a c a p a c i t o r
between the e m i t t e r
and
c o l l e c t o r of the p h o t o c e l l .
photocurrent charges the c a p a c i t o r , each s u c c e s s i v e
connected
As
the
electron
must do more work i n overcoming the f o r c e of r e p u l s i o n between
i t s e l f and
the e l e c t r o n s already
on the c a p a c i t o r .
enough e l e c t r o n s have accumulated on
impossible
for a photoelectron
Eventually
the c a p a c i t o r to make i t
to reach the c o l l e c t o r .
The
2 C. Ramsauer, Annalen der Physik, v o l . 45 (1914), p. 961,
c i t e d i n Hughes and DuBridge, P h o t o e l e c t r i c Phenomena, p. 24.
15
p o t e n t i a l d i f f e r e n c e across
the c a p a c i t o r may be measured
d i r e c t l y with an electrometer
or by u s i n g
equation 1.3.
Since
an e l e c t r o n l o s e s k i n e t i c energy eV i n overcoming a p o t e n t i a l
d i f f e r e n c e V which i s due to a f o r c e of r e p u l s i o n , the maximum
p o t e n t i a l d i f f e r e n c e across
K
M
the c a p a c i t o r , V , i s
M
a measure of
and
eV
M
= hf - p
(2.3)
The method commonly used to determine
i s t o apply a
known r e t a r d i n g p o t e n t i a l d i f f e r e n c e V between the e m i t t e r and
c o l l e c t o r which the p h o t o e l e c t r o n s must overcome i n order t o
reach the c o l l e c t o r .
T h i s p o t e n t i a l d i f f e r e n c e i s a measure
of the amount of work an e l e c t r o n must do i n order to reach the
c o l l e c t o r , f o r the e l e c t r o n has l o s t an amount of energy eV
upon r e a c h i n g
the c o l l e c t o r .
e l e c t r o n s with v a r y i n g
which i n i t i a l l y
When the e m i t t e r
i s illuminated,
k i n e t i c energies are released,
and those
have more energy than eV can reach the c o l l e c t o r .
V may be v a r i e d u n t i l a photocurrent ceases to flow.
value of V which j u s t stops the most e n e r g e t i c
The
e l e c t r o n s , V^,
i s again a measure of the maximum k i n e t i c energy of the photoe l e c t r o n s and equation 2.3 again a p p l i e s .
V
M
i s not determined s o l e l y by the a p p l i e d
potential difference.V.,
however.
retarding
There i s a l s o a contact
A
potential difference V
between the e m i t t e r
and c o l l e c t o r .
understand t h i s contact
p o t e n t i a l d i f f e r e n c e , the d i s t r i b u t i o n
of e n e r g i e s of the f r e e e l e c t r o n s i n a metal must be
To
considered.
16
A metal i s composed of many atoms bound together
crystal
lattice.
associated
Each atom has
a number of e l e c t r o n s which are
s p e c i f i c a l l y with that atom, but
not appear to be a s s o c i a t e d with any
some e l e c t r o n s
If one
free
electric
of these f r e e e l e c t r o n s were to
removed from the metal i t s e l f
left
These
They are
to move w i t h i n the metal under the i n f l u e n c e of any
i n the metal.
do
atom i n p a r t i c u l a r .
e l e c t r o n s are the f r e e or conduction e l e c t r o n s .
field
in a
a net p o s i t i v e charge would
be
be
i n the metal, s i n c e i n i t i a l l y there are equal amounts of
p o s i t i v e and
negative
charge.
i n removing i t to overcome the
e l e c t r o n and
The
Work must be done on the e l e c t r o n
f o r c e of a t t r a c t i o n between the
the net p o s i t i v e charge l e f t
behind.
d i s t r i b u t i o n of the k i n e t i c e n e r g i e s
of the
free
e l e c t r o n s i s not
the Maxwell d i s t r i b u t i o n which a p p l i e s to
k i n e t i c energies
of the molecules i n a gas.
e l e c t r o n energies
The
the
d i s t r i b u t i o n of
3
obeys the F e r m i - D i r a c s t a t i s t i c s .
The
number
of e l e c t r o n s per u n i t volume,dn,which can have k i n e t i c energy
between E and
E + dE i s given by
the
relation
3nE^dE
dn =
At a b s o l u t e
2E
3
/
2
for E < E
(2.4)
F
zero of temperature the e l e c t r o n s w i l l have the
lowest p o s s i b l e energy allowed and
3 L. A. DuBridge, New T h e o r i e s
P a r i s , Hermann and Co. , 1935, pT
so w i l l f i l l
up
the energy
of the P h o t o e l e c t r i c E f f e c t ,
7~!
17
band to a c e r t a i n value E
temperature i n c r e a s e s
but
the upper
sharply
limit
defined.
p
c a l l e d the Fermi energy.
These d i s t r i b u t i o n s a r e shown i n f i g u r e 2.1.
at i n f i n i t y
be the r e f e r e n c e
p o t e n t i a l energy of a f r e e e l e c t r o n .
it
T - 1500 K
The F e r m i - D i r a c d i s t r i b u t i o n of k i n e t i c e n e r g i e s
of the f r e e e l e c t r o n s i n a metal. N(E)dE i s the
t o t a l number of e l e c t r o n s with k i n e t i c energy
between E and E + dE. 5
Let a p o i n t
finity
little,
of the energy d i s t r i b u t i o n becomes l e s s
N(E)
2.1
As the
the average e l e c t r o n energy changes
N(E)
Figure
4
i s attracted
A free
point
f o r the
e l e c t r o n at i n -
toward the metal by the net p o s i t i v e charge
has l e f t i n the metal, and l o s e s p o t e n t i a l energy as i t
approaches the metal.
zero at i n f i n i t y
level,
If the p o t e n t i a l energy of the e l e c t r o n i s
and i t f a l l s i n t o the metal a t the Fermi energy
i t w i l l have a p o t e n t i a l energy of magnitude -p, s i n c e
an amount of work p must be done on the e l e c t r o n
from the metal back t o i n f i n i t y .
to take i t
T h i s amount of work p i s c a l l e d
4 B. I. Bleaney and B. Bleaney, E l e c t r i c i t y and Magnetism,
Oxford U n i v e r s i t y P r e s s , London, 1957, p~. 84.
5 G. P. Harnwell and J . J . L i v i n g o o d , Experimental Atomic
P h y s i c s , New York, McGraw-Hill, 1933, p. 214.
18
the work f u n c t i o n of the metal.
Consider two metals, A and B, c l o s e together i n a vacuum
but not i n c o n t a c t .
Let the work f u n c t i o n of A be p^,and that of
B be p , and the Fermi energy of A be E
and that of B be
2
If an e l e c t r o n i n A with energy E_. i s removed from the metal to
FA
i n f i n i t y i t gains p o t e n t i a l energy p^.
If i t then f a l l s i n t o
B at the E
FB
level,
i t l o s e s p o t e n t i a l energy p .
2
net change i n p o t e n t i a l energy i s p
the contact p o t e n t i a l d i f f e r e n c e V
- p .
Thus, i t s
The q u a n t i t y
called
between metals A and B i s
c
d e f i n e d by the r e l a t i o n
eV
c
= p
x
- p
(2.5)
2
I f , on the other hand, the two metals are p l a c e d i n cont a c t , no energy must bo s u p p l i e d to t r a n s f e r an e l e c t r o n from
A to B.
Let
be g r e a t e r than p^.
Then e l e c t r o n s at the E
l e v e l have g r e a t e r p o t e n t i a l energy than those at the E
level
FA
and e l e c t r o n s w i l l flow from B i n t o A.
T h i s flow w i l l c o n t i n u e
u n t i l the p o t e n t i a l energy d i f f e r e n c e caused by the net p o s i t i v e
charge remaining i n B and the net n e g a t i v e charge accumulating
i n A i s equal and o p p o s i t e to the i n i t i a l p o t e n t i a l
difference.
This i s i l l u s t r a t e d
in figure
2.2.
energy
19
i
Potential
Energy
0
P
l
P
>
;
Electron
Flow
/ /
>
Metal A
F i g u r e 2.2
c
the work f u n c t i o n of the e m i t t e r
i n going from the e m i t t e r
C
- eV
c
Metal B
than that of the c o l l e c t o r .
V
2
t
- Contact p o t e n t i a l d i f f e r e n c e V due to
flow between two metals i n c o n t a c t .
In p r a c t i c e
energy.
P
PI
if/
/
1
2
An e l e c t r o n
to c o l l e c t o r ,
electron
is
smaller
l o s e s p o t e n t i a l energy
and thus gains k i n e t i c
The c o n t a c t p o t e n t i a l d i f f e r e n c e i s an a c c e l e r a t i n g
one.
opposes the a c t i o n of V . and
A
V
M "
\ -C
V
(2
- >
6
It must be noted that V and V are both p o t e n t i a l d i f f e r e n c e s
M
A
A
between c o l l e c t o r
with respect
and e m i t t e r
to the e m i t t e r .
v a l u e s of V , V , and V
M
A
c
and are n e g a t i v e when measured
Equation 2.6
a p p l i e s to
absolute
only.
I n s p e c t i o n of equation 2.3
shows that at
some frequency
of l i g h t ^ , the energy of the photons i s equal to the work
f u n c t i o n of the
emitter
hfo
= P.
(2.7)
20
The frequency
f
c
i s c a l l e d the t h r e s h o l d frequency
L i g h t with frequency
l e s s than f
from the metal no matter
how
D
cannot
of the metal.
release electrons
i n t e n s e t h i s l i g h t may be.
Equation 2.3 may be w r i t t e n i n the form
eV
- hf - h f
M
V^j may r e a d i l y be determined
as a f u n c t i o n of V.
(2.8)
e
by p l o t t i n g photocurrent I
Since i n p r a c t i c e V
i s not known with
a degree of c e r t a i n t y , i t i s u s u a l to o b t a i n V
from t h i s
graph.
A
When V i s l a r g e and p o s i t i v e a l l of the p h o t o e l e c t r o n s reach
the c o l l e c t o r and I remains constant as V i s i n c r e a s e d .
photocurrent
i s s a i d to be s a t u r a t e d .
The
The p h o t o e l e c t r o n s have
k i n e t i c e n e r g i e s r a n g i n g from zero to KM . As V becomes r e t a r d i n g , fewer and fewer p h o t o e l e c t r o n s reach the c o l l e c t o r and the
photocurrent decreases u n i f o r m l y to zero.
The expected
graph i s
shown i n f i g u r e 2.3.
I
Saturated
V
A
Photocurrent
V
F i g u r e 2.3 - Photocurrent I as a f u n c t i o n of a p p l i e d p o t e n t i a l
d i f f e r e n c e V between e m i t t e r and c o l l e c t o r .
21
A c c o r d i n g to the c l a s s i c a l theory of e l e c t r o n s i n a metal,
the k i n e t i c e n e r g i e s of the f r e e e l e c t r o n s are too s m a l l to take
i n t o c o n s i d e r a t i o n and
so a d e f i n i t e amount of energy p must
s u p p l i e d to the e l e c t r o n s to remove them from the metal.
be
The
maximum energy of the p h o t o e l e c t r o n s should be a s h a r p l y d e f i n e d
v a l u e , and
the photocurrent
- p o t e n t i a l d i f f e r e n c e curve
approach the h o r i z o n t a l a x i s at a f i n i t e angle.
found
that t h i s was
should
When M i l l i k a n
not the case, he a t t r i b u t e d the e r r o r to
s m a l l amounts of s c a t t e r e d l i g h t of high frequency,
and
ignored
the s m a l l e r r o r r e s u l t i n g . * '
7
A c c o r d i n g to the Sommerfeld Theory
, however, some e l e c t r o n s
a l r e a d y have enough energy at room temperature to put them above
the Fermi
energy l e v e l .
from the metal
I t i s p o s s i b l e to remove these e l e c t r o n s
by doing an amount of work l e s s than p.
In
p r a c t i c e , the maximum energy of the p h o t o e l e c t r o n s i s not a
s h a r p l y d e f i n e d value, f o r some p h o t o e l e c t r o n s can have e n e r g i e s
up to 1/40
e l e c t r o n - v o l t g r e a t e r than
at room
temperature.
The r e s u l t i n g u n c e r t a i n t y i s s m a l l enough to i g n o r e at room
temperature,
but
i s temperature dependent and does i n c r e a s e
with an i n c r e a s e i n
temperature.
A number of other f a c t o r s can a l s o a l t e r the shape of the
I-V curve.
captures few
If the geometry of the c o l l e c t o r i s such that i t
e l e c t r o n s e a s i l y , s a t u r a t i o n w i l l not occur
6 R. A. M i l l i k a n , "A D i r e c t Determination of Planck's
The P h y s i c a l Review, s e r i e s 2, v o l . 7 (1916), pp. 368 7 DuBridge, New
T h e o r i e s , p.
6.
until
'h',"
369.
22
values of V are a p p l i e d which are much l a r g e r than that
to s a t u r a t e the c u r r e n t i n the i d e a l case.
r e f l e c t i o n of e l e c t r o n s or secondary
It i s p o s s i b l e that
emission of e l e c t r o n s can
occur at the c o l l e c t o r , again making i t necessary
l a r g e r values of V than expected
necessary
to apply
to achieve s a t u r a t i o n .
If
the work f u n c t i o n of the c o l l e c t o r i s small enough, emission
of e l e c t r o n s from the c o l l e c t o r can occur from r e f l e c t e d
light
giving r i s e to reverse currents.
Such r e v e r s e c u r r e n t s can cause l a r g e e r r o r s i n the
d e t e r m i n a t i o n of V^.
If V i s r e t a r d i n g f o r p h o t o e l e c t r o n s
emitted by the e m i t t e r , i t i s a c c e l e r a t i n g f o r p h o t o e l e c t r o n s
emitted from the c o l l e c t o r .
Such p h o t o e l e c t r o n s w i l l be
ed by the e m i t t e r c a u s i n g a photocurrent
ion.
i n the o p p o s i t e
collectdirect-
The
value of V. obtained from the I-V curve i n d i c a t e s
A
when these two p h o t o c u r r e n t s are equal but o p p o s i t e . The a c t u a l
value of V. occurs when photocurrent from the e m i t t e r becomes
A
zero, and i s l a r g e r than the apparent V..
The problem i s f u r t h e r
A
compounded by the f a c t that i n the r e g i o n of V , photocurrent
A
from the c o l l e c t o r i s much more dependent upon i n t e n s i t y of
light
than i s photocurrent
dependent upon l i g h t
from the e m i t t e r .
intensity.
resulting uncertainty i n V
The only way
Thus
becomes
to reduce the
i s to reduce t h i s r e v e r s e c u r r e n t .
A
The
2.4.
I-V curve f o r the case of r e v e r s e c u r r e n t i s shown i n f i g u r e
23
I
Actual V
y
Apparent V
F i g u r e 2.4
- C h a r a c t e r i s t i c s of a p h o t o c e l l with r e v e r s e c u r r e n t .
In determining
necessary
the frequency
of the l i g h t used, i t i s
to ensure that no l i g h t of g r e a t e r frequency
than that
being s t u d i e d i s i n c i d e n t upon the e m i t t e r , s i n c e such
light
would g i v e r i s e to p h o t o e l e c t r o n s of g r e a t e r energy than
being s t u d i e d .
If l i g h t of frequency
those
l e s s than that being
s t u d i e d i s i n c i d e n t upon the e m i t t e r , p h o t o e l e c t r o n s with
less
energy than those being s t u d i e d w i l l be emitted, but w i l l
not
reach the c o l l e c t o r i n the r e g i o n of V .
photoelectrons a l t e r
affect
energy
the shape of the I-V curve, but i n no
the value of
The
These lower
way
V..
A
values of V
f o r s e v e r a l f r e q u e n c i e s of l i g h t
having
A
been measured, a p l o t of V
equations 2.3
and
2.6
as a f u n c t i o n of f may
are combined, equation 2.9
eV
M
= hf - p
be made.
may
be
If
obtained.
(2.3)
(2.6)
eV
A
= hf - p + e V
(2.9)
c
A p l o t of V as a f u n c t i o n of f i s a s t r a i g h t l i n e whose s l o p e
A
is h/e.
The accpeted value of h/e i s 4.14 x 1 0 ^
volt-seconds.
-1
-19
Using the accepted
calculated
value of e,
from t h i s
The i n t e r c e p t
In equation 2.9
1.6
x 10
coulombs, h may be
slope.
w i t h the V
the i n t e r c e p t
M
a x i s i n equation 2.3
is
-p/e.
with the V a x i s i s - p / e + V .
A
C
If the accepted value of p f o r the emitter i s known, V f o r the
' C
p h o t o c e l l may be c a l c u l a t e d from the l a t t e r i n t e r c e p t .
25
CHAPTER 3.
EXPERIMENTAL INVESTIGATIONS AND RESULTS.
The experimental i n v e s t i g a t i o n s focussed on two major
questions.
used.
The f i r s t of these concerned the apparatus
to be
A p h o t o c e l l , a means of i s o l a t i n g s e v e r a l s p e c t r a l
a means of changing l i g h t i n t e n s i t y , and instruments to
small currents
lines,
measure
had to be found which c o u l d be put together
i n t o an experiment r e a d i l y performed by secondary s c h o o l
students.
The second major q u e s t i o n concerned the method to be u s e d .
methods were apparent.
and c o l l e c t o r
The p o t e n t i a l d i f f e r e n c e between
emitter
c o u l d be v a r i e d and the photocurrent measured,
the p h o t o c e l l c o u l d be used to charge a c a p a c i t o r
mum p o t e n t i a l d i f f e r e n c e a c r o s s i t measured.
had to y i e l d a reasonable r e s u l t
students.
Two
or
and che maxi-
The method chosen
and be e a s i l y repeated by
The procedures f o l l o w e d and r e s u l t s
obtained are
out-
l i n e d below.
3.1
Photocells.
The f i r s t p h o t o c e l l i n v e s t i g a t e d was that manufactured by
the Leybold Company.
T h i s p h o t o c e l l has an emitter
of a l a y e r of potassium on the i n s i d e of
collector
consisting
the g l a s s w a i l .
i s a p l a t i n u m wire i n the shape of a c i r c u l a r
The c o l l e c t o r
has e l e c t r i c a l
pass an e l e c t r i c
T h i s process
current
the emitter
to evaporate
The e l e c t r i c a l
to
any i m p u r i t i e s .
i s c a l l e d " f l a s h i n g " the p h o t o c e l l i n the
and the e x t e r n a l
loop.
connections e n a b l i n g the user
through i t
p r o v i d e d with the p h o t o c e l l .
The
literature
c o n n e c t i o n between
c i r c u i t i s w e l l i n s u l a t e d from the
26
housing of the p h o t o c e l l t o prevent
leakage c u r r e n t s .
p h o t o c e l l i s i l l u m i n a t e d through a small hole
The
housing i t s e l f
The
i n the housing.
i s grounded t o s h i e l d the p h o t o c e l l from any
external e l e c t r o s t a t i c e f f e c t s .
Three such p h o t o c e l l s were t e s t e d .
cell
having been i n use f o r some time.
c e l l s were new.
The other
two photo-
The c o l l e c t o r on one of these had been bent out
of i t s c i r c u l a r shape e i t h e r i n being
however.
The f i r s t was an o l d
manufactured or shipped,
The c h a r a c t e r i s t i c s of the o l d and new p h o t o c e l l s
shown i n f i g u r e s 3.1 and 3.2 were taken under s i m i l a r c o n d i t i o n s .
The
c h a r a c t e r i s t i c s of the p h o t o c e l l w i t h the d i s t o r t e d c o l l e c t o r
did
not vary
significantly
from those of the other
F i g u r e 3.1 shows the l a r g e r e v e r s e
experienced w i t h the o l d e r p h o t o c e l l .
were e s p e c i a l l y evident
c u r r e n t s which were
These r e v e r s e
with an u l t r a - v i o l e t
apparent c u t - o f f v o l t a g e V
new p h o t o c e l l .
forultra-violet
light
currents
source.
The
l i g h t was c o n s i s t -
A
e n t l y found to be between V
f o r blue
l i g h t and V
A
l i g h t , a r e s u l t a t t r i b u t e d t o the r e v e r s e
shows that the r e v e r s e
f o r green
A
current.
Figure
3.2
c u r r e n t s were much s m a l l e r when the new
p h o t o c e l l s were used.
The
o l d p h o t o c e l l was f l a s h e d s e v e r a l times i n an attempt
to reduce the r e v e r s e
current.
At no time d i d the reverse
current
decrease a f t e r f l a s h i n g , and at one time the r e v e r s e
current
increased.
The new p h o t o c e l l s were not f l a s h e d .
An o p t i c a l system was devised
which reduced the l a r g e
27
I Scale:
e
I
F i g u r e 3.1
- C h a r a c t e r i s t i c s of o l d Leybold c e l l .
Current
measured with K e i t h l e y e l e c t r o m e t e r .
V = p o t e n t i a l d i f f e r e n c e between c o l l e c t o r and
ground.
F i g u r e 3.2
- C h a r a c t e r i s t i c s of new Leybold c e l l s .
Current
measured on K e i t h l e y e l e c t r o m e t e r .
V = p o t e n t i a l d i f f e r e n c e between c o l l e c t o r and
ground.
V
28
reverse
current
experienced with the o l d e r p h o t o c e l l .
of l i g h t approximately one centimeter
onto the plane of the c o l l e c t o r
r e a c h i n g the c o l l e c t o r .
i n diameter was focussed
r e d u c i n g the amount of l i g h t
C u r r e n t s of the order of 10 ^
were produced by t h i s spot s o u r c e ,
the e m i t t e r
The r e v e r s e
by two major
c u r r e n t was s m a l l and the same area of
c o u l d be used f o r a l l measurements keeping the work
f u n c t i o n of the e m i t t e r
constant.
It was thought at one p o i n t that the r e v e r s e
be of t h e r m i o n i c o r i g i n .
dry i c e ,
ampere
but the disadvantage of having
to measure such a s m a l l c u r r e n t was l a r g e l y o f f s e t
advantages.
A spot
The p h o t o c e l l housing was packed i n
but no s i g n i f i c a n t change i n r e v e r s e
Since the magnitude of a c u r r e n t
as the temperature
c u r r e n t may
decreases,
c u r r e n t was n o t e d .
of t h e r m i o n i c o r i g i n decreases
i t was concluded that, t h e . r e v e r s e
c u r r e n t was not t h e r m i o n i c i n o r i g i n .
Four commercial p h o t o c e l l s were i n v e s t i g a t e d .
Their
main advantage was thaj: they were much l e s s expensive than the
Leybold p h o t o c e l l .
1P39,
and 5581,
Three of these p h o t o c e l l s , numbers
were s i m i l a r i n c o n s t r u c t i o n ,
929,
having an e m i t t e r
shaped l i k e part of a c y l i n d e r coated w i t h a composite of mate r i a l s and separated
collector
from the g l a s s w a l l of the p h o t o c e l l .
i n each case was a s i n g l e post i n f r o n t of the
With such a d e s i g n i t was very d i f f i c u l t
emitter.
to i l l u m i n a t e the
e m i t t e r without i l l u m i n a t i n g the c o l l e c t o r
teristics
The
as w e l l .
The c h a r a c -
of the 929 and 1P39 p h o t o c e l l s were very s i m i l a r and
are shown i n f i g u r e 3 . 3 .
The c h a r a c t e r i s t i c s
of the 5581,
a gas
I Scale:
Blue - 1 u n i t
Green - 1 u n i t
Mercury l i g h t source
Stark f i l t e r s
0,
0,
•6
x 10
amp,
x 10" •7 amp.
3.0
2.0
F i g u r e 3.3
- C h a r a c t e r i s t i c s of 929 and 1P39 commercial photocells.
Current measured with K e i t h l e y e l e c t r o m e t e r .
3.0
F i g u r e 3.4
- C h a r a c t e r i s t i c s of 5581 commercial p h o t o c e l l .
Current measured with K e i t h l e y e l e c t r o m e t e r .
30
f i l l e d p h o t o c e l l , are shown i n f i g u r e
3.4.
None of these p h o t o c e l l s was c o n s i d e r e d s u i t a b l e f o r
experiment.
F i g u r e 3.4
shows that the 5581
had l a r g e r e v e r s e c u r r e n t s .
upon i n t e n s i t y .
currents
The other
In any c a s e ,
p h o t o c e l l apparently
V
was found to depend
two p h o t o c e l l s had l a r g e
f o r high i n t e n s i t y l i g h t .
this
reverse
These r e v e r s e c u r r e n t s
were
probably due to the f a c t that the whole p h o t o c e l l was f l o o d e d
with l i g h t .
No way c o u l d be found, however,
c e l l s without o b t a i n i n g r e v e r s e c u r r e n t s .
values of h/e obtained u s i n g the 929
sistently
too low.
Furthermore,
and 1P39 c e l l s were c o n -
reasons.
A commercial p h o t o c e l l , number 926,
was found whose
was a d i s c mounted to one s i d e of the e m i t t e r
T h i s arrangement
and at
were s t i l l
o b t a i n e d , however,
p h o t o c e l l c o n t a i n i n g che c o l l e c t o r
characteristics
of t n i s c e l l are
collector
right
angles
allowed the p h o t o c e l l to be
i l l u m i n a t e d without i l l u m i n a t i n g the c o l l e c t o r .
currents
the
It was concluded that these p h o t o c e l l s were
u n s u i t a b l e f o r these
to the e m i t t e r .
to i l l u m i n a t e these
Large r e v e r s e
even with the end of
masked w i t h tape.
shown i n f i g u r e
the
The
3.5.
It was concluded from these i n v e s t i g a t i o n s that the Leybold
p h o t o c e l l was b e t t e r s u i t e d f o r t h i s experiment
commercial p h o t o c e l l s
3.2
F i l t e r s and L i g h t
than any of
the
investigated.
Sources.
The problem was to i s o l a t e
intense spectral
l i n e s so that
31
V
Figure
3.5
(Volts)
- C h a r a c t e r i s t i c s o f 926 p h o t o c e l l f o r two
intensities
o f b l u e and g r e e n l i g h t .
C u r r e n t measured w i t h
Keithley electrometer.
32
no l i g h t of frequency higher than that being s t u d i e d would
reach the e m i t t e r .
The mercury spectrum was chosen because of
the presence of t h r e e s t r o n g l i n e s , the wavelengths of which are
3650A" ( u l t r a - v i o l e t ) ,
4360 A ( b l u e ) ,
and 5460 A ( g r e e n ) .
5890 A l i n e of the sodium spectrum was a l s o used.
spectrum had l e s s i n t e n s e l i n e s as w e l l ,
The
The mercury
but no attempt was
made t o i s o l a t e or use t h e s e .
Since a s m a l l spot of l i g h t was needed to reduce the reverse
current,
an i n t e n s e
l i g h t source was needed.
For t h i s
reason
the low power mercury l i g h t source p r e s e n t l y a v a i l a b l e i n the
secondary s c h o o l s was not found t o be s a t i s f a c t o r y .
reasonably l a r g e p h o t o c u r r e n t s ,
To o b t a i n
the Leybold p h o t o c e l l had to
be completely f l o o d e d w i t h l i g h t from t h i s source and l a r g e
reverse
currents
resulted.
A mercury a r c lamp was used f o r the
measurements made i n t h i s i n v e s t i g a t i o n .
Two s e t s of f i l t e r s were i n v e s t i g a t e d .
c o n s i s t e d of three Corning g l a s s f i l t e r s ,
filter,
The f i r s t
set
an u l t r a - v i o l e t
a b l u e - p a s s f i l t e r and a green-pass
filter.
The l i g h t
passed by each of these f i l t e r s was i n s p e c t e d w i t h a d i r e c t
v i s i o n spectrometer.
The green-pass
f i l t e r passed no l i g h t of
s h o r t e r wavelength than the 5460 A mercury l i n e .
The b l u e - p a s s
f i l t e r was found to pass the 4046 A and 4077 A l i n e s as w e l l as
the 4360 A l i n e .
ultra-violet
For t h i s reason i t was not s u i t a b l e .
f i l t e r passed no v i s i b l e l i g h t other
The
than the
4046 A and the 4077 A l i n e s which were extremely weak.
These
33
f i l t e r s were found to have a f u r t h e r disadvantage
i n that i t
was p o s s i b l e f o r l i g h t to enter the p h o t o c e l l without being
first
filtered.
The other
set of f i l t e r s
with the low power mercury
T h i s set c o n s i s t s
like material.
referred
direct
i n v e s t i g a t e d was that p r o v i d e d
l i g h t source r e f e r r e d
of four f i l t e r s made of a f l e x i b l e
L i g h t p a s s i n g through these f i l t e r s
to as the Stark f i l t e r s )
v i s i o n spectrometer.
4360 A l i n e ,
to above.
was a l s o
plastic(to be
i n s p e c t e d with a
The b l u e - p a s s f i l t e r
i s o l a t e d the
the green-pass f i l t e r allowed no l i g h t of
shorter
o
wavelength than 5460 A through, but the two yellow
o
filters
f a i l e d t o e l i m i n a t e the 5460 A l i n e i n order to i s o l a t e
5770 A l i n e .
These f i l t e r s
c o u l d be taped r i g h t
the
over the open-
i n g i n the housing and so f i l t e r e d a l l l i g h t e n t e r i n g the photocell.
They are r e a d i l y a v a i l a b l e i n most secondary
was t h e r e f o r e
schools.
concluded that the Stark f i l t e r s were s u i t a b l e
f o r i s o l a t i n g the blue and green l i n e s of the mercury
A check was made to determine
filter
passed any u l t r a - v i o l e t
Corning u l t r a - v i o l e t
filter.
violet
It
i f the Stark
light.
spectrum.
blue-pass
T h i s blue f i l t e r and the
f i l t e r were used together as a compound
Since i t had a l r e a d y been determined that the u l t r a f i l t e r passed no blue l i g h t , and l i g h t p a s s i n g both
had to be u l t r a - v i o l e t .
No measureable
photocurrent
filters
was observed.
It was concluded that the Stark b l u e - p a s s f i l t e r does not pass
ultra-violet
light.
An attempt was a l s o made to o b t a i n a photocurrent
using
34
the mercury
l i g h t source and red f i l t e r m a t e r i a l .
of the order of I O
- 1 1
ampere was observed.
A photocurrent
It was concluded
that the Leybold p h o t o c e l l i s i n s e n s i t i v e to red l i g h t ,
such a s m a l l photocurrent
of s h o r t e r
since
c o u l d w e l l be due to s c a t t e r e d
light
wavelength than 6000 A .
An attempt was made to e l i m i n a t e the need f o r f i l t e r s by
i s o l a t i n g the s p e c t r a l
l i n e s with a crude monochromator.
from the mercury arc was passed through the d i r e c t
Light
vision
spectrometer and focussed onto the p h o t o c e l l .
Although r e a s o n -
able r e s u l t s
were not
ucible,
were obtained once,
and the c u r r e n t s
by a f a c t o r of at
these r e s u l t s
reprod-
produced by the p h o t o c e l l were s m a l l e r
l e a s t ten than those produced u s i n g the
A simple method was found to reduce s c a t t e r e d l i g h t
the p h o t o c e l l .
At a l l times when measurements
the room was completely darkened.
p l a c e d between the small c i r c u l a r
The paper had a hole i n i t j u s t
of l i g h t .
housing,
With the f i l t e r
i t was reasonably
that being i n v e s t i g a t e d
A p i e c e of black paper was
l i g h t source and the p h o t o c e l l .
large
certain
A problem was encountered
enough to pass the
the
that l i t t l e
result
A neutral
spot
photocell
l i g h t other
than
emitter.
i n changing l i g h t
intensity
without a l t e r i n g the shape of the spot or the s p e c t r a l
of the l i g h t .
reaching
were being made
taped over the hole i n the
reached
filters.
quality
f i l t e r was t r i e d but abandoned when no
c o u l d be obtained f o r the u l t r a - v i o l e t
light.
The method
35
f i n a l l y used was to reduce
the area of the f o c u s s i n g q u a r t z
lens u s i n g stops of black paper.
Each stop c o n s i s t e d of a black
paper d i s c the s i z e of the l e n s .
The d i s c had a hole cut i n i t ,
the i n t e n s i t y of the l i g h t passed being d i r e c t l y p r o p o r t i o n a l to
the area of the h o l e .
lens.
The stops were taped over the f o c u s s i n g
T h i s method not o n l y reduced the i n t e n s i t y without
altering
the q u a l i t y of the l i g h t , but a l s o ensured that the same area of
the e m i t t e r
was used throughout keeping the work f u n c t i o n con-
s t a n t w i t h i n reasonable
limits.
It was concluded from these i n v e s t i g a t i o n s
that a s t r o n g
mercury a r c source used with the Stark blue and green
i s o l a t e d the 4360 A and 5460 A* l i n e s of the mercury
The 3650 A l i n e c o u l d be
filcers
spectrum.
i s o l a t e d u s i n g an u l t r a - v i o l e t
filter.
The i n t e n s i t y of the l i g h t c o u l d best be changed by changing
the a p e r t u r e of the f o c u s s i n g lens by means of paper
stops
taped over the l e n s .
3.3
Method.
3.3a
Current Measuring Method.
The i n i t i a l
attempts to perform the experiment
by measuring photocurrent
were made
as a f u n c t i o n of the a p p l i e d p o t e n t i a l
d i f f e r e n c e V between emitter
and c o l l e c t o r .
Characteristics
such as those shown i n f i g u r e s C l and 3.2 were o b t a i n e d .
cutoff
voltage
difference
V
A
was i n t e r p r e t e d
The
as being the a p p l i e d p o t e n t i a l
f o r which the photocurrent
became z e r o ,
A major problem soon became evident whenever
large
reverse
36
c u r r e n t s were encountered
found on the graph.
current
f o r the t r u e value of V i s net
A
The p o t e n t i a l d i f f e r e n c e at
easily
which the
became zero was i n f a c t the p o t e n t i a l d i f f e r e n c e at which
the photocurrent
and the r e v e r s e c u r r e n t
were e q u a l .
This
effect
was e s p e c i a l l y evident i n the case of u l t r a - v i o l e t l i g h t f o r
which V was found to l i e between V f o r blue and V f o r green.
A
A
A
Because the r e v e r s e c u r r e n t was so l a r g e f o r the u l t r a - v i o l e t
l i g h t the t r u e value of V was l a r g e r than the value i n d i c a t e d
A
on the graph.
Because of the l a r g e r e v e r s e c u r r e n t s t h i s method
—16
y i e l d e d values of h/e r a n g i n g from 7.5 x 10~
volt-seconds
-15
i20% to 5.0
ency.
x 10
v o l t - s e c o n d s ±20% w i t h no apparent
T h i s method was t h e r e f o r e
It was then noted that part
current
abandoned.
of the p o t e n t i a l d i f f e r e n c e
-
curve always appeared to be l i n e a r and that the photo-
c e l l a p p a r e n t l y obeyed Ohm's law i n a c e r t a i n
f u r t h e r noted that s t r a i g h t
p o r t i o n s of the curves
the same p o i n t .
region.
l i n e s drawn through the
It
was
linear
f o r v a r i o u s i n t e n s i t i e s of the same
frequency of l i g h t i n t e r s e c t e d
at
consist-
the p o t e n t i a l d i f f e r e n c e
This i s i l l u s t r a t e d in figure
axis
3.6.
The p h o t o c e l l was t r e a t e d as a d e v i c e obeying Ohm's law.
The p o i n t of i n t e r s e c t i o n
as V ^ .
of the s t r a i g h t
l i n e s was
interpreted
With the Leybold c e l l and the green and blue l i n e s of
-15
mercury,
h/e was found to be 4.3
with t h i s i n t e r p r e t a t i o n
x 10
of the a a t a .
v o l t - s e c o n d s ±20%
No r e s u l t
i n g f u l c o u l d be obtained w i t h the u l t r a - v i o l e t
that was mean-
light,
however.
The major problem encountered u s i n g t h i s i n t e r p r e t a t i o n
of
37
I Scale:
F i g u r e 3.6
1 U n i t = 1.0
x 10
amp.
- C h a r a c t e r i s t i c s f o r v a r i o u s i n t e n s i t i e s of blue
l i g h t u s i n g Leybold c e l l .
I measured with K e i t h l e y
electrometer.
V i s p o t e n t i a l of c o l l e c t o r with
r e s p e c t to ground.
38
the data was l a c k of c o n s i s t e n c y
i n the r e s u l t s .
u s i n g the Leybold c e l l and the spectrometer
A measurement
used as a mono-
— 15
chromator
y i e l d e d h/e = 4 . 0 x 10
weeks l a t e r
v o l t - s e c o n d s 120%.
u s i n g the same apparatus
Several
and procedure the value of
had i n c r e a s e d by approximately one v o l t and h/e was found
be 3.3
x 10
1
5
v o l t - s e c o n d s ^20%.
The change i n the
value
obtained f o r h/e may not have been s i g n i f i c a n t s i n c e the
tainties
A
c e r t a i n l y was s i g n i f i c a n t .
Since no
reason c o u l d be found to e x p l a i n why any part
should be s t r a i g h t ,
the data cannot
theoretical
of the
curve
i t was concluded that t h i s i n t e r p r e t a t i o n
be j u s t i f i e d .
To support t h i s c o n c l u s i o n ,
was found i n many cases that the p o i n t of i n t e r s e c t i o n
of
of
it
the
l i n e w i t h the p o t e n t i a l d i f f e r e n c e a x i s d i d depend
upon l i g h t
3.3b
uncer-
i n the two values o v e r l a p p e d , but the change i n the
value of V
straight
to
intensity.
C a p a c i t o r Method.
The theory of t h i s method has been d i s c u s s e d i n chapter
A capacitor
was connected between the e m i t t e r
and the K e i t h l e y e l e c t r o m e t e r
and the
2.
collector
on open c i r c u i t was used to
measure V . At f i r s t i t was hoped that the commercial p h o t o M
c e l l s c o u l d be used with t h i s method.
It was found t h a t ,
u s i n g the 929,
IP39, and 926 p h o t o c e l l s ,
the l i g h t i n t e n s i t y .
V was a f u n c t i o n of
M
It was concluded that the Leybold photo-
c e l l was again s u p e r i o r .
An optimum s i z e d c a p a c i t o r
had to be found to be used
w i t h the Leybold p h o t o c e l l .
Since t h i s p h o t o c e l l produces
-10
c u r r e n t s as s m a l l as 10
ampere, a one m i c r o f a r a d c a p a c i t o r
4
needs a time of the order of 10
Thus the c a p a c i t a n c e
of
seconds or a few hours to
must be s m a l l to be p r a c t i c a l .
charge.
Measurements
were made f o r the blue and green l i n e s of the mercury
spectrum under o p t i c a l c o n d i t i o n s s i m i l a r to those d e s c r i b e d i n
section 3.2.
These measurements are given i n t a b l e
BLUE LIGHT
full
3.1.
GREEN LIGHT
lower
int.
low
int.
full
int.
lower
.int.
low
int.
Capacitance
int.
Nil
Nil
5 x 10"
farad
2 x IO
farad
1 x 10~
farad
1.08
0.97
1.30
1.30
0.84
0.73
0.81
0.97
1.11
0.65
0.63
0.55
1.07
1.05
1.05
0.72
0.90
1.00
0.65
0.68
0.68
0.30
0.28
0.24
0.75
0.74
0.74
0.26
0.25
0.20
1 n
iU
- 9
b
Table 3.1
- Maximum p o t e n t i a l d i f f e r e n c e V i n v o l t s a c r o s s
c a p a c i t o r s charged with a Leybold p h o t o c e l l .
From t a b l e 3.1
it
both by the c a p a c i t a n c e
can be seen that V„ was determined
M
and the i n t e n s i t y of the l i g h t .
was decided that the 5 x 10
capacitor
1 0
f a r a d (500
gave the most c o n s i s t e n t
l e n g t h s of time.
this capacitor
results within
took no more than f i v e minutes to
ment of h/e was made.
l i n e was 2.6
micro m i c r o f a r a d )
x 10"
reasonable
For example, w i t h very low i n t e n s i t y
Using t h i s c a p a c i t o r
1 5
It
light
charge.
and a new Leybold p h o t o c e l l a measure-
The best
s l o p e of the V - frequency
M
v o l t - s e c o n d s t20%.
T h i s value i s very low.
40
Since
was d e f i n i t e l y a f u n c t i o n of l i g h t i n t e n s i t y ,
and the
value of h/e obtained was too s m a l l , t h i s method was a l s o
aban-
doned.
3.3c F i n a l
Result.
A r e t u r n to the o r i g i n a l method with the new Leybold
p h o t o c e l l s r e v e a l e d very much smalLer r e v e r s e c u r r e n t s .
a quartz lens r e s u l t s
green,
were obtained f o r u l t r a - v i o l e t ,
blue,
and yellow l i g h t which were much more reasonable
those o b t a i n e d with the o l d e r p h o t o c e l l .
used and the r e s u l t s
3.4
Using
than
T h i s method was
finally
obtained are o u t l i n e d i n Chapter 4.
Methods of Measuring Small C u r r e n t s .
Since the Leybold p h o t o c e l l produced c u r r e n t s
as l O
- 1
as s m a l l
^ ampere a method of measuring these s m a l l c u r r e n t s
to be e s t a b l i s h e d .
Two e l e c t r o n i c
e l e c t r o m e t e r with a decade
The f i r s t
circuit
shown i n f i g u r e 3.7.
circuits
had
and a K e i t h l e y
shunt were u s e d .
t r i e d was the twin t r i o d e bridge
circuit
41
Its
I. i n
0 volts
F i g u r e 3.7 - Twin t r i o d e b r i d g e
With no c u r r e n t
circuit.
f l o w i n g i n t o the input of t h i s
circuit
the 2000 ohm p o t e n t i a l d i v i d e r can be adjusted so that there i s
zero p o t e n t i a l d i f f e r e n c e a c r o s s galvanometer
G.
When c u r r e n t
flows i n t o the c i r c u i t and through the 10 megohm r e s i s t o r R-^
the p o t e n t i a l of the g r i d on one t r i o d e i s a l t e r e d
the c u r r e n t
p a s s i n g through t h i s t r i o d e .
remains unchanged.
resistor
meter.
R
?
flows through the 33,000 ohm
A p o t e n t i a l d i f f e r e n c e thus appears
of a c u r r e n t
triode
changing the p o t e n t i a l of one s i d e of the galvano-
meter and a c u r r e n t
register
This current
The other
changing
flows through i t .
i n the g r i d c i r c u i t
Thus,
a c r o s s the galvanothe i n t r o d u c t i o n
causes the galvanometer
to
a current.
T h i s c i r c u i t worked reasonably w e l l f o r c u r r e n t s
as s m a l l
42
as 10
-9
ampere i f a s e n s i t i v e galvanometer was u s e d .
galvanometer's
s e n s i t i v i t y was 5.5
s e n s i t i v e range.
advantages.
x 10
The
amp/cm on i t s most
The c i r c u i t was found to have two main d i s -
The major problem was encountered w i t h the
p o i n t which had a tendency to wander s l o w l y .
In t h i s
zero
situation
i t was not p o s s i b l e to determine i f an apparent change i n c u r r e n t
was due to a r e a l change i n c u r r e n t
of the c i r c u i t .
or due to t h i s i n s t a b i l i t y
The other disadvantage was that the s e n s i t i v i t y
of the c i r c u i t was determined d i r e c t l y by the s e n s i t i v i t y of
galvanometer used.
In g e n e r a l ,
galvanometers
the
s u i t a b l e f o r use
i n t h i s experiment are not to be found i n secondary
schools.
Other than these problems, the c i r c u i t was found to be s u i t a b l e
f o r use i n t h i s
experiment.
The second c i r c u i t
with t r a n s i s t o r s
t r i e d r e p l a c e d the twin t r i o d e
tube
i n an attempt to c o r r e c t the tendency of
zero p o i n t to wander.
This c i r c u i t
i s shown i n f i g u r e
3.8.
+6
4.7K
4.7K
I in
o->Tl
270
T2
LK
o
volts
4.7K
kl
^
T
4
T3
1.8K
10K
T l , T2, T3, T4 a l l
T1417 t r a n s i s t o r s .
F i g u r e 3.8
the
T r a n s i s t o r c i r c u i t to measure s m a l l
0 volts
currents.
43
T h i s c i r c u i t works b a s i c a l l y on the same p r i n c i p l e as
twin t r i o d e b r i d g e .
The 270
ohm p o t e n t i a l d i v i d e r can be adjusted
so there i s zero p o t e n t i a l d i f f e r e n c e a c r o s s the
When a c u r r e n t
i s introduced i t
T^ which t u r n s the c u r r e n t
t u r n s the c u r r e n t
on through T .
the balance and the galvanometer
condition.
The t r a n s i s t o r s
the s e n s i t i v i t y of the
the
galvanometer.
on through
This current
upsets
r e g i s t e r s t h i s unbalanced
are arranged i n tandem to
increase
circuit.
T h i s c i r c u i t was not as s e n s i t i v e as the twin t r i o d e
bridge,
and was not u s e f u l i n measuring c u r r e n t s
smaller
than
—8
10~
still
ampere.
Moreover, the zero p o i n t of the
fluctuated.
The c i r c u i t was t h e r e f o r e
no improvement over the twin t r i o d e b r i d g e
The K e i t h l e y e l e c t r o m e t e r
abandoned as being
circuit.
proved to be the most u s e f u l
instrument f o r measuring the s m a l l c u r r e n t s
Leybold p h o t o c e l l .
galvanometer
produced by the
The zero p o i n t of the instrument d i d not
wander and c o u l d e a s i l y be checked again a f t e r each
C u r r e n t s of the order of 1 0
relative
measurement.
ampere c o u l d be measured w i t h
- 1 0
ease and r e l i a b i l i t y .
d e t e r m i n a t i o n of h/e i n Chapter
T h i s instrument was used f o r
the
4.
3.5
Summary.
1.
The Leybold p h o t o c e l l was found to y i e l d a reasonable and
consistent
value of h/e when used w i t h the K e i t h l e y
and a spot source of l i g h t .
electrometer
The commercial p h o t o c e l l s i n v e s t i -
44
gated gave r e v e r s e c u r r e n t s
2.
A s t r o n g mercury
which made them u n r e l i a b l e .
l i g h t source used with the f i l t e r s supp-
l i e d w i t h the Stark low power mercury
l i g h t source i s o l a t e d
green and blue l i n e s of the mercury spectrum.
Intensity
could
best be changed by changing the a p e r t u r e of the f o c u s s i n g
The l i g h t had to be concentrated
had to be s h i e l d e d from s t r a y
3.
The c u r r e n t
cell
light.
method.
The K e i t h l e y e l e c t r o m e t e r was the most r e l i a b l e
f o r measuring the s m a l l c u r r e n t s
instrument
produced by the Leybold c e l l .
The t w i n - t r i o d e b r i d g e c i r c u i t was s u i t a b l e ,
advantages .
lens.
- measuring method proved to be much more
r e l i a b l e than the c a p a c i t o r
4.
i n a s m a l l spot and the
the
but had some d i s -
45
CHAPTER 4.
A PHOTOCELL DETERMINATION OF PLANCK'S CONSTANT.
The apparatus and method having been decided upon a measurement of h/e was made.
was t w o f o l d .
The purpose i n making t h i s
It was necessary
measurement
to ensure that the p h y s i c s i n v o l v e d
i n the experiment was c o r r e c t and that the q u a n t i t y being measured
was r e a l l y h / e .
At the same time the r e s u l t s
to be expected
from the experiment under optimum c o n d i t i o n s c o u l d be o b t a i n e d .
4d
Method.
The apparatus was assembled as shown i n f i g u r e 4 . 1 .
p h o t o c e l l c a s i n g was clamped down to the t a b l e so that
The
the
chance of an a c c i d e n t a l change i n the p h o t o c e l l ' s p o s i t i o n was
minimal.
The e l e c t r i c a l
electrometer
lead from the e m i t t e r
was kept as short as p o s s i b l e to reduce p o s s i b l e
leakage c u r r e n t s .
The e n t i r e apparatus
housing was grounded to a water p i p e .
i n c l u d i n g the p h o t o c e l l
In the o p t i c a l
a q u a r t z l e n s was used to ensure passage
light.
of the
system,
ultra-violet
L i g h t i n t e n s i t y was changed by the use of the b l a c k
paper stops d e s c r i b e d i n s e c t i o n 3 . 2 .
a d i s t a n c e of twice i t s
and
to the K e i t h l e y
The lens was p l a c e d at
f o c a l l e n g t h from both the p h o t o c e l l
the l i g h t source so that a spot of l i g h t the same s i z e
the source c o u l d be focussed onto the plane of the
collector
keeping the amount of l i g h t i n c i d e n t on the c o l l e c t o r
as p o s s i b l e .
A b l a c k paper screen was p l a c e d a few
i n f r o n t of the l i g h t s o u r c e .
as
as s m a l l
centimeters
T h i s screen had a hole i n i t
enough to pass the l i g h t beam to the p h o t o c e l l , but served
large
to
46
,
PAP£R
SCREEN
4i/
FM/TTfift
L(S«T
F i g u r e 4.1
(b)
- Optical
system.
47
reduce the s c a t t e r e d l i g h t r e a c h i n g the p h o t o c e l l .
no windows and was completely dark other
l i g h t source.
throughout.
blue,
The room had
than the l i g h t from the
The Leybold p h o t o c e l l and i t s mount were used
The mercury arc
lamp was used f o r the
ultra-violet,
and green l i g h t , and a sodium lamp f o r the yellow l i g h t .
A Corning u l t r a - v i o l e t
pass f i l t e r was used f o r the
and Stark f i l t e r s used f o r the b l u e , green,
It was necessary to apply a c o r r e c t i o n
ultra-violet
and y e l l o w .
to the
potential
d i f f e r e n c e measured to o b t a i n the p o t e n t i a l d i f f e r e n c e
emitter
and c o l l e c t o r .
current
by p a s s i n g the c u r r e n t
The K e i t h l e y e l e c t r o m e t e r measures
through a standard r e s i s t a n c e and
measuring the p o t e n t i a l d i f f e r e n c e a c r o s s the r e s i s t o r .
p o t e n t i a l d i f f e r e n c e was s u b t r a c t e d
measured,
from the p o t e n t i a l
that between the c o l l e c t o r
the p o t e n t i a l d i f f e r e n c e
No c o r r e c t i o n
between
This
difference
and the ground, to o b t a i n
between the c o l l e c t o r
and the
emitter.
was made f o r c o n t a c t p o t e n t i a l d i f f e r e n c e as
this
q u a n t i t y was unknown.
Data f o r two i n t e n s i t i e s
of each frequency of l i g h t were
p l o t t e d d i r e c t l y on graphs and are
4.4,
and 4 . 5 .
of l i g h t are
shown i n f i g u r e s 4 . 2 ,
F u r t h e r data f o r a g r e a t e r v a r i e t y
to be found i n appendix A .
of
intensities
These are not i n c l u d e d
here because the q u a r t z lens was not used and the l i g h t
was v a r i e d u s i n g a n e u t r a l
4.2
4.3,
intensity
filter.
Results.
A graph of s t o p p i n g p o t e n t i a l d i f f e r e n c e V. as a f u n c t i o n
A
Figure 4.1
3650 A L i n e
I Scale:
V
(c)
- Apparatus f o r p h o t o c e l l
experiment.
(Hg)
1 u n i t = 1.0
x 10
-9
amp
(Volts)
F i g u r e 4.2
- Ultra-violet
(f
-1.0
-0.5
1.4 v o l t s
14
-1
8.2 x 10
seconds
)
V
F i g u r e 4.3
- Blue (f - 6.9
x 10
A
= 1.0
seconds
)
volts
5.0
F i g u r e 4.6
6.0
7.0
8.0
- R e l a t i o n s h i p between s t o p p i n g p o t e n t i a l
9.0
and frequency.
51
of l i g h t frequency f i s shown i n f i g u r e 4 . 6 .
along a s t r a i g h t
l i n e w i t h i n experimental u n c e r t a i n t y .
r e l a t i o n s h i p between V
- k f + k
A
x
The
(4.1)
2
i s the s l o p e of the graph and k
when f i s
lie
and f thus has the form
A
V
where k,
The p o i n t s
i s the value of V
A
zero.
L i n e s of maximum and minimum s l o p e were drawn through
points.
The maximum slope AV /At was found to be 3.8
x
the
10"
1 5
A
-15
volt-seconds,
seconds.
and the minimum s l o p e to be 3.7
From equation 2.3
x 10
t h i s slope i s h / e .
volt-
Therefore
h = e
and
h
h
Thus
m a x
rain
h
= 1.6
= 6.1
=
1
,
6
= 5.9
x 10
x 10
x
-19
~\A
x 10 **
10
-
(4.2)
-15
c o u l x 3.8 x 10
joule-seconds.
c
4
o
~
joule-seconds.
u
1
x
3
« (6.0 i 0.1) x 1 0 ~
7
34
x
1
0
1
5
volt-seconds.
volt-seconds.
joule-seconds.
T h i s measured value of h d i f f e r s from the accepted
value
-34
6.6
x 10
joule-seconds
by 9%.
The u n c e r t a i n t y quoted i n the
measured value of h r e f l e c t s only the u n c e r t a i n t y
and not any s y s t e m a t i c
From equation 2 . 9 ,
i n the
slope
error.
k
is -p/e + V_.
The value of k
Q
is
given by
0.4
v o l t s = 3.8
x 10
-15
volt-seconds
x 5.5
x 10
14
seconds
-1
+
(4.3)
52
where the p o i n t f o r green l i g h t xn f i g u r e 4.6
has been used.
Therefore
k
2
The value of p / e i s 1;8
V
= k
= -1.7
volts
f o r potassium.,
+ p/e = - 1 . 7
= 0.1
volts
v o l t s + 1.8
1
Therefore
volts
volts.
Since the work f u n c t i o n of platinum i s g r e a t e r than 6.2
2
volts,
electron
the contact p o t e n t i a l d i f f e r e n c e between platinum and
potassium should be of the order of 4 to 5 v o l t s .
4.3
D i s c u s s i o n of
The f i r s t
Results.
important
f a c t evident
from the r e s u l t s
V was independent of the i n t e n s i t y of the
A
f a c t was f u r t h e r
A where,
magnitude of the photocurrent
than 0.05
l i g h t used.
emphasized i n the data presented
f o r four i n t e n s i t i e s
was that
This'
i n appendix
each of green and blue l i g h t ,
v a r i e d , but V v a r i e d by no more
A
volt.
It was a l s o evident that V. was a l i n e a r f u n c t i o n of
A
Since only four p o i n t s on the graph were found, however,
evidence s u p p o r t i n g t h i s c o n c l u s i o n was not at a l l
The main source of e r r o r
the r e v e r s e c u r r e n t .
ultra-violet
light.
f.
the
strong.
i n t h i s d e t e r m i n a t i o n of h was
T h i s r e v e r s e current
was l a r g e r
for
the
and blue l i g h t than i t was f o r the green and yellow
For the u l t r a - v i o l e t
the value of V
A
I B . I. Bleaney and B. Bleaney, E l e c t r i c i t y and Magnetism,
Oxford U n i v e r s i t y P r e s s , London, 1957, p . 86.
2 Ibid.,
the
p.
86.
and blue l i g h t ,
53
chosen was i n f a c t the value of V f o r which photocurrent
and
r e v e r s e c u r r e n t were e q u a l , and the t r u e value of V was probably
A
a little
larger
than the value chosen.
If t h i s were the
the measured value of the s l o p e should be lower than
as was found.
systematic
Thus the r e v e r s e c u r r e n t
case,
expected
s u p p l i e s the major
error.
The s m a l l value of the contact p o t e n t i a l d i f f e r e n c e between
the emitter
and c o l l e c t o r
may account
f o r the r e v e r s e
This small contact p o t e n t i a l d i f f e r e n c e i n d i c a t e s
f u n c t i o n of the p l a t i n u m c o l l e c t o r
currents.
that the work
was not as l a r g e as
expected
and so the t h r e s h o l d frequency of the platinum wire was i n the
r e g i o n of the f r e q u e n c i e s being used i n t h i s experiment.
platinum wire was thus capable of g i v i n g r i s e
current
the r e v e r s e
?
to i t s own photo-
current.
The other major source
of e r r o r was due to the
uncertainty
i n i d e n t i f y i n g the f r e q u e n c i e s of l i g h t r e s p o n s i b l e f o r
results.
The
The Stark f i l t e r s appeared to i s o l a t e
the
the blue and
green l i n e s of mercury reasonably w e l l as f a r as c o u l d be
mined by examining the l i g h t they passed w i t h a d i r e c t
spectroscope.
It
is doubtful,
however,
completely e l i m i n a t e s the two v i o l e t
deter-
vision
i f the blue f i l t e r
l i n e s i n the neighbourhood
o
of 4050 A .
T h i s l i g h t has a higher frequency than that of
blue l i g h t b e i n g s t u d i e d and may be the cause of V
A
the
being a
l i t t l e higher than expected, the p o i n t f o r blue being a l i t t l e
above the s t r a i g h t l i n e through the other p o i n t s on the V - f
A
graph shown i n f i g u r e 4 . 6 .
54
It
i s of i n t e r e s t to compare these r e s u l t s w i t h those
obtained by Hansen and C l o t f e l t e r
apparatus.
1
u s i n g the complete Leybold
They found that the data obtained were a sharp
f u n c t i o n of the time i n t e r v a l between h e a t i n g the
axid t a k i n g the d a t a .
In a l l cases the values of h/e
were lower than the accepted v a l u e .
present
The r e s u l t s
obtained
obtained i n the
study d i f f e r from those obtained by Hansen and C l o t f e l t e r
i n that the data are more c o n s i s t e n t
V
collector
and f i s more d e f i n i t e l y
and the r e l a t i o n s h i p
between
linear.
A
4.4
Conclusions.
1.
The r e l a t i o n s h i p between the s t o p p i n g p o t e n t i a l
V. and the frequency of l i g h t f i s
difference
linear.
A
2.
V
3.
The r e l a t i o n s h i p between V and f has the form
A
A
i s independent of the i n t e n s i t y of the
light.
V - k f + k
A
1
2
where k
and k
are c o n s t a n t s .
to that i n equation
This r e l a t i o n s h i p i s
similar
3.2.
-15
4.
The value of k^ was found to be 3.8
x 10
which i s 9% lower than the accepted value of
5.
Assuming k^ to be h / e ,
joule-seconds.
volt-seconds
h/e.
h was found to be (6.0
t 0.1)
x
10~
T h i s value i s 9% below the accepted v a l u e .
1 R. J . Hansen and B. E . C l o t f e l t e r , " E v a l u a t i o n of Commercial
Apparatus f o r Measuring h / e , " American J o u r n a l of P h y s i c s ,
v o l . 34 (1966), p . 77.
34
55
6.
The contact p o t e n t i a l d i f f e r e n c e between e m i t t e r and c o l l e c t o r
of the Leybold p h o t o c e l l was found to be 0 . 1 v o l t .
7.
The c h i e f sources of s y s t e m a t i c
c u r r e n t and the u n c e r t a i n t y
of the
8.
e r r o r are due to the r e v e r s e
i n the d e t e r m i n a t i o n of the frequency
light.
The major c o n c l u s i o n reached i s that a p h o t o c e l l experiment
d e v e l o p i n g the concepts i n v o l v e d i n the quantum model of l i g h t
i s f e a s i b l e f o r use i n secondary s c h o o l s .
c r i b e d i n t h i s chapter
The experiment d e s -
i s capable of y i e l d i n g r e s u l t s which
are
i n agreement w i t h the major p o i n t s i n the theory of the photoelectric
effect.
Such an experiment i n v o l v e s techniques and
i n s t r u m e n t a t i o n very s i m i l a r to that encountered by the
i n h i s p r e v i o u s experimental work.
student
The data c o l l e c t e d by the
student can be analyzed u s i n g g r a p h i c a l a n a l y s i s with which the
student i s very f a m i l i a r .
cost of a p p a r a t u s ,
of time necessary
It
is likely
The only major problems i n v o l v e
the
s e v e r a l hundreds of d o l l a r s , and the amount
to assemble the apparatus and c o l l e c t
data.
that four to f i v e hours of experimental work w i l l
be r e q u i r e d to do the e n t i r e
experiment.
56
CHAPTER 5.
5.1
A PHOTOCELL EXPERIMENT FOR SECONDARY SCHOOL PHYSICS.
Introduction.
S e c t i o n 29 of A Laboratory
d e a l s with the t o p i c s
photoelectric
Course i n P h y s i c s ,
to which t h i s experiment
Book Two
is related.
The
e f f e c t i s i n t r o d u c e d by s h i n i n g u l t r a - v i o l e t
on a z i n c p l a t e attached to an e l e c t r o s c o p e .
the e l e c t r o s c o p e l o s e s negative
1
It
light
i s noted that
charge but does not l o s e
positive
2
charge.
In the ensuing d i s c u s s i o n r e f e r e n c e i s made to the
3
4
two PSSC f i l m s , Photons
and I n t e r f e r e n c e of Photons
i n which
evidence of the e x i s t e n c e of quanta of l i g h t or photons
presented.
is
At t h i s p o i n t the r e l a t i o n s h i p between the maximum
k i n e t i c energies
of p h o t o e l e c t r o n s
used i s d i s c u s s e d .
and the frequency of
The f o l l o w i n g experiment
i s meant to
light
replace
this discussion.
The experiment
quantitative.
Its
itself
i s meant to be more q u a l i t a t i v e
purpose i s to lead the student
c l u s i o n that the maximum p h o t o e l e c t r o n
the i n t e n s i t y of i n c i d e n t
light,
energy
to the
light.
con-
i s independent of
but that a l i n e a r
relationship
e x i s t s between t h i s maximum energy and the frequency of
incident
than
The twin t r i o d e b r i d g e c i r c u i t
the
i s used because
1 D. L . L i v e s e y , G. H . Cannon, and T . Ryniak, A Laboratory
Course i n P h y s i c s , Part Two, Vancouver, Copp C l a r k ,
1965,
pp. 158 - 178.
2 Ibid.,
p.
159.
3 P h y s i c a l Science Study Committee, T e a c h e r ' s Guide to
PSSC F i l m s , New York, Modern L e a r n i n g A i d s ,
1963.
4
Ibid.
the
57
it
i s r e l a t i v e l y easy to c o n s t r u c t
i s not an instrument
5.2
and the Kexthley
found i n most secondary
schools.
The Experiment.
The p h o t o e l e c t r i c
effect
can best be s t u d i e d under more
c o n t r o l l e d c o n d i t i o n s than were present with the
experiment
by u s i n g a p h o t o c e l l .
These e l e c t r o n s
electroscope
The back of the p h o t o c e l l
coated w i t h potassium and emits e l e c t r o n s
it.
electrometer
can be c o l l e c t e d
is
when l i g h t shines on
by the platinum loop i n
the p h o t o c e l l i f the platinum loop i s made p o s i t i v e w i t h r e s p e c t
to the potassium s u r f a c e .
Study the c i r c u i t
shown i n f i g u r e 5.1.
The p l a t i n u m loop can be made e i t h e r
p o s i t i v e or negative by
a d j u s t i n g the p o t e n t i a l d i v i d e r R .
(Review S e c t i o n
The very s m a l l c u r r e n t
26.B.2.)
produced by the p h o t o c e l l must be
measured u s i n g the twin t r i o d e b r i d g e c i r c u i t
In the twin t r i o d e b r i d g e a c u r r e n t
or an
electrometer.
through R s e t s up a p o t e n t i a l
2
d i f f e r e n c e between the g r i d and cathode of one s i d e of the
a l t e r i n g the c u r r e n t
in current
This
causes a p o t e n t i a l d i f f e r e n c e to appear a c r o s s
galvanometer
current.
passed by that s i d e of the tube.
and the galvanometer
indicates
the presence
R^ can be a d j u s t e d so that the galvanometer
zero when no c u r r e n t
i s p a s s i n g through R .
tube
change
the
of
reads
the
l"
Wire the c i r c u i t
twin t r i o d e
a quartz
shown i n f i g u r e 5 . 1 .
Adjust R
b r i d g e so that the galvanometer
reads z e r o .
l e n s between the p h o t o c e l l and a mercury a r c
that both the lamp and the p h o t o c e l l are at
twice
i n the
the f o c a l
l e n g t h of the
lens.
a distance
Arrange
lamp so
equal
to
DO NOT LOOK DIRECTLY AT THE
MERCURY LAMP AND DO NOT EXPOSE THE PHOTOCELL TO THE FULL INTENSITY
OF THE LIGHT.
it
about
P l a c e a l a r g e p i e c e of cardboard w i t h a hole i n
1 cm. i n diameter
directly
i n front
lamp so that l i g h t shines through the h o l e .
of the
mercury
C a r e f u l l y focus
the
image of the hole onto the potassium s u r f a c e so that no l i g h t
s h i n e s on the p l a t i n u m l o o p .
to the
How l a r g e i s t h i s image
compared
object?
14
Tape the blue f i l t e r
(frequency
= 6.9
x 10
/second)
across
\
59
the opening i n the p h o t o c e l l h o u s i n g .
Darken the room and measure
the photocurrent as the p o t e n t i a l d i f f e r e n c e between the
and c o l l e c t o r of the p h o t o c e l l i s v a r i e d .
as a f u n c t i o n of p o t e n t i a l d i f f e r e n c e .
d i f f e r e n c e d i d the c u r r e n t
emitter
P l o t a graph of
current
For what p o t e n t i a l
f i r s t become zero?
To e x p l a i n why t h i s p o t e n t i a l d i f f e r e n c e i s
negative
assume that each photon s t r i K l n g the p h o t o c e l l g i v e s a l l of
energy to an e l e c t r o n .
energy K.
its
Each e l e c t r o n then emerges with k i n e t i c
In t r a v e l l i n g toward the c o l l e c t o r which i s at
p o t e n t i a l of - V with respect
to the e m i t t e r ,
a
each e l e c t r o n
k i n e t i c energy eV where e i s the charge on the e l e c t r o n .
p o t e n t i a l d i f f e r e n c e f o r which the c u r r e n t becomes z e r o ,
loses
The
V ,
i s the p o t e n t i a l d i f f e r e n c e f o r which the i n i t i a l k i n e t i c energy
K equals eV .
To determine the e f f e c t
of l i g h t i n t e n s i t y upon K, cut
s e v e r a l d i s c s of b l a c k paper the same s i z e as the l e n s .
h o l e s of v a r i o u s s i z e s i n t h e s e .
effect
Cut
P l a c e one over the l e n s .
does i t have on the image?
What
P l o t s e v e r a l more graphs of
photocurrent versus p o t e n t i a l d i f f e r e n c e f o r v a r i o u s i n t e n s i t i e s
of l i g h t .
What e f f e c t
does changing l i g h t i n t e n s i t y have on the
s i z e of the photocurrent at any g i v e n voltage?
effect
be e x p l a i n e d i n terms of photons?
changing i n t e n s i t y have on V ?
k i n e t i c e n e r g i e s of the
How can t h i s
What e f f e c t
does
How does i n t e n s i t y a f f e c t
the
photoelectrons?
Repeat the experiment w i t h s e v e r a l i n t e n s i t i e s of u l t r a
60
violet
light
(f = 8.2
x 1 0 / s e c o n d s ) and green l i g h t
14
(f -
5.5
14
x 10
/seconds).
P l o t a graph of V
What i s the r e l a t i o n s h i p between V
as a f u n c t i o n of
and f ?
T h i s r e l a t i o n s h i p can be w r i t t e n i n the form eV
where eV
i s the k i n e t i c energy of the e l e c t r o n s ,
energy of the photons,
electrons
first
the wave theory
by E i n s t e i n i n 1905
hf i s
the
T h i s equation was
and d i r e c t l y
contradicts
of l i g h t which says that the energy of the
depends upon i n t e n s i t y .
A c c o r d i n g to t h i s r e l a t i o n s h i p
k i n e t i c energy r e c e i v e d by the e l e c t r o n s
frequency,
= hf - p
and p r e p r e s e n t s the work done by the
i n escaping from the potassium.
suggested
frequency.
not upon the i n t e n s i t y .
Planck's constant.
light
the
depends only upon
The constant h i s
called
Measure the s l o p e of your graph, o b t a i n an
estimate of h/e and hence of h .
Note that f o r some value of f ,
V
becomes z e r o .
This
value of f i s c a l l e d the t h r e s h o l d frequency because no matter
what the i n t e n s i t y ,
l i g h t with frequency lower than the
h o l d frequency cannot
Estimate
this
produce p h o t o e l e c t r o n s .
the t h r e s h o l d frequency of potassium.
light?
can produce a
thres-
Why i s t h i s
What c o l o r
so?
is
Try l i g h t of t h i s c o l o r on the c e l l and see i f you
photocurrent.
B I B L I O G R A P H Y
62
BIBLIOGRAPHY
Aussenegg, F . "A Simple Method f o r the Determination of P l a n c k ' s
C o n s t a n t , " A c t a P h y s i c a A u s t r i a c a , v o l . 14 (1961),
pp. 440 - 44T"!
Bleaney, B. I . , and Bleaney, B. E l e c t r i c i t y and Magnetism.
London, Oxford U n i v e r s i t y P r e s s , 1957.
B r i t i s h Columbia, Department of E d u c a t i o n , D i v i s i o n of C u r r i c ulum. Senior Secondary School S c i e n c e , P h y s i c s 12. 1965.
D a v i s , S. P. " P h o t o e l e c t r i c E f f e c t E x p e r i m e n t . " American J o u r n a l
of P h y s i c s , v o l . 29 (1961), p p . 706 - 707.
Dubridge, L . A . New T h e o r i e s of the P h o t o e l e c t r i c
Hermann and C o . , 1935.
Effect.
Paris,
E i n s t e i n , A . " L i g h t Generation and L i g h t A b s o r p t i o n . " Annalen
der P h y s i k , v o l . 20 (1906), p p . 199 - 206.
H a r n w e l l , G. P . , and L i v i n g o o d , J . J . Experimental Atomic
P h y s i c s . New York, M c G r a w - H i l l , LU3in
Hansen, R. J . , and C l o t f e l t e r , B. E . " E v a l u a t i o n of Commercial
Apparatus f o r Measuring h / e . " American J o u r n a l of P h y s i c s ,
v o l . 34 (1966), p p . 75 - 78.
Hughes, A . L . "On the Emission V e l o c i t i e s of P h o t o - E l e c t r o n s . "
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s e r i e s A, v o l . 2 1 2 ( 1 9 1 3 ) , p p . 2 0 5 - 2 2 6 .
Hughes, A . L . , and DuBridge, L . A . P h o t o e l e c t r i c
New York, M c G r a w - H i l l , 1932.
Phenomena,
L e n a r d , P. "The P r o d u c t i o n of Cathode Rays by U l t r a - v i o l e t
Annalen der P h y s i k , v o l . 2 (1900), p p . 359 - 375.
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L i v e s e y , D . L . , Cannon, G. H . , and Ryniak, T . A Laboratory
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Course
M i l l i k a n , R. A . "A D i r e c t P h o t o e l e c t r i c Determination of P l a n c k ' s
h . " The P h y s i c a l Review, s e r i e s 2, v o l . 7 (1916), p p . 355 388.
P h y s i c a l Science Study Committee. T e a c h e r ' s
F i l m s . New York, Modern L e a r n i n g A i d s ,
Guide to the PSSC
1963.
63
R i c h a r d s o n , 0. W., and Compton, K. T . "The P h o t o e l e c t r i c E f f e c t . "
P h i l o s o p h i c a l Magazine, s e r i e s 6, v o l . 24 (1912), p p . 575 Suhrmann, R. "Determination of P l a n c k ' s Constant as a Q u a l i t a t i v e
Lecture Experiment."
P h y s i k a l i s c h e Z e i t s c h r i f t , v o l . 33
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P h i l o s o p h i c a l Magazine, s e r i e s 5, v o l . 48 (1899), p p . 547 -
'SET.
A P P E N D I X
A
Leybold c e l l c h a r a c t e r i s t i c s
i n t e n s i t i e s of blue l i g h t .
m
5 0
for
(4 u n i t s = 1.0
x 10
amp)
0
V. = 1.05 t 0.05 v o l t s .
A
Data taken w i t h g l a s s l e n s and
neutral f i l t e r .
0
-2.5
-2.0
-1.5
V ( V o l t1—
s)
0.5
1.0
to
5 0
Leybold c e l l c h a r a c t e r i s t i c s
i n t e n s i t i e s of green l i g h t .
V = 0.06
A
A
+ 0.10
-2.0
various
volts.
Data taken w i t h g l a s s
neutral f i l t e r .
—©—
for
1.5
l e n s and
-0.5
A P P E N D I X
B
SPECIAL APPARATUS AND CATALOGUE NUMBERS
Leybold p h o t o c e l l
Leybold 558
77
Housing f o r Leybold p h o t o c e l l
Leybold 558
78
Low power mercury
and f i l t e r s
Canlab
3400
Welch
3720G
Mercury a r c
lamp
light
source