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Physics 404: First Midterm Test
Name (
print
):
"I pledge on my honor that I have not given or received any unauthorized assistance on this examination."
March 11, 2008
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Honor Pledge:
Don't get bogged down on any problem you find difficult.
Skip ahead and go through all 4 pages,
then come back to it afterwards!!
If you find a question ambiguous, ask the TA and/or write a short
explanation of why.)
1. Short answer or multiple choice (in which case, circle the correct answer):
a) What is the probability that a particle has not scattered by time 2
τ
?
0
1/2
1/4
e
-1
e
-2
e
-4
< 0.00001
b) What is k
B
T (to one significant digit) for T = 100 K?
Indicate clearly which unit of energy you are
using!
c)) Rewrite the thermal conductivity
κ
in terms of
τ
rather than
λ
.
2. Suppose a system has 3 possible energies: 0,
ε
, and 2
ε
.
a) Write the general expression for
⟨
E
⟩
in this case.
(No derivation needed.)
b) Evaluate
⟨β
E
⟩
if exp(-
βε
) = 0.1, or equivalently
βε
= 2.3.

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3. Using Stirling's approximation, show that ln [N!/(N/2)!] can be written as (N/2) times some

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