# Physics H133: Problem Set #4

Here are some hints, suggestions, and comments on the problem set.
## Two-Minute Problems

Remember to give a **good** explanation, no longer than
two sentences.

- Q4T.4: Standard interference problem! Once you know the de Broglie
wavelength, the problem goes through as with any two-slit interference
problem involving waves of that wavelength.
- Q4B.8: Is this ball relativistic or non-relativistic? Remember to make a
*comparison*. Don't just say
that the wavelength is small. Also, what determines the wavelength
size (i.e., in an alternate universe, what could be different that
would make it important to consider the wave nature of a pitched
baseball?).

## Chapter Q4 Problems

- Q4S.2: How do you go from voltage difference to kinetic energy?
(Hint: Express kinetic energy in eV.) The electrons are nonrelativistic
if K << mc
^{2}; if they are nonrelativistic, you can use
K = p^{2}/2m. For a proton, repeat with a different value
for mc^{2}.
- Q4S.7: How does the de Broglie wavelength depend on v?
You can estimate the mass of the buckeyball by noting it is 60
carbon atoms, each with 6 protons and 6 neutrons. (Don't try to
calculate it too precisely, we're only interested in a few percent
answer here.)
- Q4S.11: Do you think the de Broglie wavelength of the electrons
should come out much smaller, smaller, about the same, or larger
than the size of the nucleus? Why did Hofstadter get the Nobel
prize for this work (look it up!)? He obviously saw something
important. (c) What is the rest mass energy equivalent of an electron?
Larger or smaller than 20 GeV?
- Q4R.2: The speeds are nonrelativistic, so the ordinary
expression for the de Broglie wavelength (with the new h!) can be
applied. You'll need to estimate the spacing of interference
fringes (bright and dark spots) at the far end of the courtyard
in order to judge if it is feasible to see the interference.
Question: Does destructive interference of people hurt? :)
- Q4A.1: The relativistic formulas for energy E and momentum p
are related by E/p = c
^{2}/v, which follows immediately from
E = gamma*(mc^{2}) and p = gamma*mv, with
gamma = 1/(1-v^{2}/c^{2})^{1/2}.
(These relations can be found in R9 and follow from a Lorentz
transformation from the rest frame to a frame moving a velocity v.)
The
velocity of the crests of the waves is f*lambda. To evaluate
d(omega)/dk, you'll need to substitute the relativistic expressions
for E and p in terms of gamma and actually take the derivatives.

Your comments and
suggestions are appreciated.

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**Physics H133: Hints for Problem Set 4.**

Last modified: 01:55 pm, April 04, 2012.

furnstahl.1@osu.edu