MSE 110 Problem Set 2,
Problem 1
An electron of wavelength
λ
= 0.333 nm forms a standing wave on an orbit of radius r = 0.159.
What is the level n of that orbit? (8pts) [Answer in integer]
Ans:
From n
λ
= 2
π
r we obtain
3
333
.
0
159
.
0
2
2
=
×
×
=
=
π
λ
π
r
n
The electron is orbiting on the level of quantum number n=3.
Problem 2
Some kids are playing jump rope with a rope of length L = 6 meter and shake it hardly enough to
induce a standing wave of quantum number n=4. What is the wavelength of the induced standing
wave? (8pts) [Answer in meter]
Ans:
4 halfwavelength will fit along the rope to form the standing wave. Hence,
m
n
L
3
4
6
2
2
=
×
=
=
λ
Problem 3
A guitar string of length 1 meter is banged hardly enough to induce a standing wave of quantum
number n=12. What is the wavelength of the induced wave? (5pts) [Answer in meter]
Ans:
12 halfwavelength will fit along the guitar string to form the standing wave. Hence,
m
n
L
166
.
0
12
1
2
2
=
×
=
=
λ
1
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Problem 4
Which of the following orbital has a spherical geometry. (6pts) [answer A, B, C, D]
A:
2d
B:
3s
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 Spring '07
 Lucas
 Standing wave, 1 meter, 2 L, 0.166 M

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