Name:
Answer
€
€
€
€
€
Quiz
1
October
18,
2010
TA:
Robert
20A
Disc
1B
1. The
electron
in
a
hydrogen
atom
is
initially
at
a
distance
4
Å
from
the
proton,
and
then
moves
to
a
distance
of
3
Å
from
the
proton.
A)
Calculate
the
change
in
the
force
between
the
proton
and
the
electron.
(15
pts)
F(r)
=
q1q2/4πε0r2
ΔF
=
F(3
Å)
–
F(4
Å)

(−1.602 *10−19 C)(1.602 *10−19 C) 
1
1
ΔF =
−

−12 2 −1 −1
−10
2
−10
2
4 π (8.854 *10 C J m )  (3*10 m) (4 *10 m) 
ΔF
=
‐1
*10‐9
N
B)
Calculate
the
change
in
the
potential
energy
between
the
proton
and
the
electron.
(15
pts)
V(r)
=
q1q2/4πε0r
ΔV
=
V(3
Å)
–
V(4
Å)

(−1.602 *10−19 C)(1.602 *10−19 C) 
1
1
ΔV =
−


−12 2 −1 −1
−10
−10
4 π (8.854 *10 C J m )  3*10 m 4 *10 m 
ΔV
=
‐1.92
*10‐19
J
2. KXLU
88.9
FM
is
a
college
radio
station
in
Los
Angeles
that
broadcasts
at
a
frequency
of
88.9
MHz.
Calculate
the
wavelength
and
energy
of
the
radio
waves.
(10
pts)
c
E = hν = h λ
c 2.998 *10 8 m /s
=
3.37
m
λ= =
υ
88.9 *10 6 /s
E = hυ = (6.626 *10−34 J • s)(88.9 *10 6 /s) =
5.89
*10‐26
J
3. A)
Use
the
Bohr
model
to
calculate
the
radius
and
the
energy
of
the
C5+
ion,
a
one
electron
species,
in
the
n
=
3
state.
(15
pts)
rn
=
(5.29
x
10‐11
m)
n2/Z
r3
=
(5.29
x
10‐11
m)
32/6
r3
=
7.94
x
10‐11
m
En
=
‐(2.18
x
10‐18
J)
Z2/n2
E3
=
‐(2.18
x
10‐18
J)
62/32
E3
=
‐8.72
x
10‐18
J/atom
B)
How
much
energy
would
be
required
to
remove
the
electrons
from
5
mol
of
C5+
in
this
state?
(10
pts)
23
‐18
E∞
=
‐5NAE3
=
‐(5
mol)(6.022
x
10 atoms/mol)(‐8.72
x
10 J/atom)
E∞
=
2.62
x
107
J
C)
What
frequency
and
wavelength
of
light
would
be
emitted
in
a
transition
form
the
n
=
3
to
the
n
=
1
state
of
this
ion?
What
is
the
name
of
the
series
where
this
transition
occurs?
(15
pts)
ΔE
=
E1
–
E3
 62 62 
−18
ΔE = 2.18 *10 J 2 − 2  =
‐6.98
*10‐17
J
1 3 
c
ΔE = hυ = h λ
ΔE
6.98 *10−17 J
=
1.05
*1017
Hz
υ=
=
h
6.626 *10 34 J • s
c 2.998 *10 8 m /s
=
3
*10‐9
m
λ= =
υ
1.05 *1017 /s
Name
of
series
=
Lyman
series
€
€
€
€
€
4. A)
Prove
that
the
De
Broglie
wavelength
equation
is
consistent
(aka,
show
that
the
units
are
the
same
on
both
sides
of
the
equation).
(10
pts)
λ=m
 kg • m 

• m • s
h
J•s
(N • m) • s  s2 
=
=
=
= m
mv kg(m /s)
kg(m /s)
kg(m /s)
m=m
B)
If
the
average
bruin
bear
weighs
27
kg,
calculate
the
de
Broglie
wavelength
of
this
bear
if
it
is
running
at
a
velocity
of
15
mph.
(10
pts)
h
6.626 *10−34 J • s
λ=
=
=
3.66
*10‐36
m
 15mi  5280 ft  1m  1hr 
mv
27kg




 hr  1mi  3.28 ft  3600s 
1
Å
=
10‐10
m
1
m
=
3.28
ft
1
mile
=
5280
ft
me
=
9.109
x
10‐31
kg
mp
=
1.673
x
10‐27
kg
mn
=
1.675
x
10‐27
kg
h
=
6.626
x
10‐34
J
s
ε0
=
8.854
x
10‐12
C2
J‐1
m‐1
c
=
2.998
x
108
m
s‐1
e
=
1.602
x
10‐19
C
F
=
ma
J
=
N
m
N
=
kg
m
s‐2
F(r)
=
q1q2/4πε0r2
Cheat
Sheet
Page
V(r)
=
q1q2/4πε0r
=
‐Ze2/4πε0r
E
=
hυ
=
hc/λ
λ
=
h/mv
=
h/p
rn
=
(5.29
x
10‐11
m)
n2/Z
En
=
‐(2.18
x
10‐18
J)
Z2/n2
Metric
Prefixes
109
=
G
106
=
M
103
=
k
10‐1
=
d
10‐2
=
c
10‐3
=
m
10‐6
=
µ
10‐9
=
n
10‐12
=
p
10‐15
=
f