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Answer Key
Ch 1a, Problem Set Three
Side 1 of 4
5 Points
5 Points
5 Points
5 Points
5 Points
Problem One – Waves – 25 Points, 5 Each
Nodes are the points where the wavefunction amplitude crosses zero at all times (not including
our boundary conditions). Therefore:
a.
Final Answer: 2 Nodes
b.
Final Answer: 3 Nodes
c.
The correspondence principle states that the more nodes a wavefunction has, the higher in
energy it is (for identical sytems, of course). Therefore:
Final Answer: B has more nodes, therefore B is higher in energy.
d.
For any wave of the system to have higher energy than B, it must have more nodes then
B. Therefore the minimum number of nodes that wave C may have is:
Final Answer: 4 Nodes
e.
The principle quantum number,
n
, is related to the number of nodes through a simple
relation:
n
=
number of nodes
+
1
Therefore, wave A with 2 nodes has
n
=3, and wave B with 3 nodes has
n
=4.
Final Answer:
n
A
=3,
n
B
=4
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View Full DocumentAnswer Key
Ch 1a, Problem Set Three
Side 2 of 4
2 Points
8 Points
3 Points
2 Points
Problem Two – Heisenberg Uncertainty principle – 15 Points
We cannot change the mass of the proton, so the uncertainty in the momemtum is wholly in the
velocity component:
"
p
x
"
x
#
h
4
$
"
p
x
=
"
mv
x
( )=
m
"
v
x
+
v
x
"
m
=
m
"
v
x
with
Δ
m going to zero.
The uncertainty in velocity (
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 Fall '08
 Lewis

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