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____________________
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Page 5 of 26
Version # 1
Continued on next page
5.
Which one of the following
is
an allowed set
of quantum numbers (
n, l, m
l
, m
s
) for an
electron?
(A)
(2, 1, 0, 1)
(B)
(3, 3, 1, –½)
(C)
(2, 1, –1, –½)
(D)
(3, –1, 1, +½)
(E)
(4, 1, 2, +½)
6.
Both X-rays and electrons can form diffraction patterns when interacting with atoms
in a solid.
What would be the
momentum p
(in kg m s
–1
) of an electron that had the
same wavelength
as an X-ray photon with a frequency of 1.5 × 10
18
Hz?
(A)
3.1 × 10
7
(B)
3.3 × 10
–24
(C)
2.6 × 10
–26
(D)
1.3 × 10
–42
(E)
3.5 × 10
–54
Refer to data page (p.25)
for de Broglie
equation (
λ
= h / mv = h / p) and mass of an
electron (m
e
= 9.10
×
10
−
31
kg).
λ
= h / p
we need:
p = h /
λ
Convert the given frequency into wavelength
(recall that
ν
and
λ
have an inverse relationship,
related through the speed of light):
λ
= c /
ν
=
2.9979
×
10
8
m/s / 1.5 × 10
18
s
−
1
λ
= 1.9
99
×
10
−
10
m
Now
p = h /
λ
p = (6.626
×
10
−
34
J s ) / (1.9
99
×
10
−
10
m)
p = 3.3
1
×
10
−
24
J s m
−
1
or kg m s
–1
Note (data page): 1 J = 1 kg m
2
s
−
2
, therefore
J s m
−
1 =
kg m
2
s
−
2
×
s m
−
1
= kg m s
–1
Boundaries on n: n = 1, 2, 3, 4, ….
Boundaries on l: l = 0, 1, 2, 3, …, n-1
Boundaries on m
l
: m
l
= -l, .
., 0, …, +l
Boundaries on m
s
: m
s
= +1/2, -1/2
(A)
incorrect m
s
value
(B)
incorrect l value
(C)
correct
(D)
incorrect l value
(E)
incorrect m
l
value