Experimental Physics EP3
Atoms and Molecules
– Atomic model –
Thomson’s model, Rutherford scattering
http://research/uni-leipzig.de/valiu/
Experimental Physics III - Atomic structure
1
Thomson’s plum padding model of atom
2R
b
b
The plum pudding model of the atom by J. J.
Thomson, who discovered the electron in
1897, was proposed in 1904 before the
discovery of the atomic nucleus in order to
add the electron to the atomic model.
E
Q
4 0r 2
Zer 3 1
 3
R 4 0 r 2
b R
2b
zZe2
    (b) 2 db 
2

R
16

Rm

0
0
b 0
Experimental Physics III - Atomic structure
 2 
n   exp 
2
 N 
2
Rutherford scattering
 cos 

y
 sin 

F cos 
F sin 
F
0

b
r

x
Particle charge
q   ze
qQ
F
4 0r 2
L  mb0  mr2
Nucleus charge
Q   Ze

dL  
 r F 0
dt
d
dt
Alpha particle in a helium chamber
 
mr   const
dt
2
r  b0
d
Experimental Physics III - Atomic structure

r

v

r
3
Rutherford scattering
 cos 

y
 sin 

F cos 
F sin 
F
0
b
r 2  b0

r

x
q' sin d  mb0d y
q'
1  cos  
y 
mb0
 y        0 sin 

sin 

2
m0 b 1  cos 
q'
zZe2
tan 
2 4 0m02b
dt
d
d x
F cos   m
dt
d y
F sin   m
dt
   0
Energy conservation
zZe2
q' 
4 0
Experimental Physics III - Atomic structure
4
Rutherford scattering
I
A
Number of particles passing
through Unit area per unit time
d
R

d
b
b
dN  Id  I 2bb
Number of particles passing through
an area element d
 2q'  cos / 2 

dN  ndI 2 
d
3
 E0  sin  / 2 
2
Number of particles per unit length nd
dN  ndI 2bb
db 2q'
1

d E0 sin 2  / 2 
A  2R sin Rd
b
2
ndI  zZe 
1


dN A 
A
2 
4

4 R  8 0 E0  sin  / 2 
2
2 q'

cot
E0
2
b 
db

d
Experimental Physics III - Atomic structure
5
Rutherford scattering
Experimental Physics III - Atomic structure
6
To remember!
 Thomson anticipated that atom is a positively charged
sphere with homogeneously distributed point-like electrons.
 Thomson’s atoms may scatter charged particles only to
small angles (Gaussian distribution for a collection of atoms).
 Rutherford scattering equation is derived under
assumption of positive charge condensed
in a center of atom.
 The main deficiency of the Rutherford
model is its inability to explain the
stability of atoms.
Experimental Physics III - Atomic structure
7