Problem Set #11 (Let`s do some Newcular Physics)

Physics 322: Modern Physics
Spring 2015
Problem Set #11
(Let’s do some Newcular Physics)
Due Friday, April 24 in Lecture
ASSUMED READING: Before starting this homework, you should have read
Chapter 8, Sections 3 and 4 and Chapter 11 Sections 1 and 2 of Harris’ Modern
Physics.
1. [Harris 8.35] Two particles in a box occupy the n=1 and n’=2 individual
particle states. Given that the normalization constant is the same as in
Example 8.2, calculate for both the symmetric and antisymmetric state the
probability that both particles would be found in the left side of the box
1
(i.e. between 0 and ! L ). Do the results make sense given what you know
2
about symmetric versus antisymmetric states.
2. [Harris 8.7] A friend asks: “Why is there an exclusion principle?”
Explain in the simplest terms.
3. [Harris 8.41 tweaked] What is the minimum possible energy for five
1
(non-interacting) spin-! particles of mass m in a one-dimensional box of
2
3
length L? What if the particles were spin-1 or spin-! ? Clearly provide
2
your explanation in words as well as mathematics. NOTE: Explicitly state
1
what happens in each of the three cases stated: spin-! , spin-1, and spin2
3
! as you describe how you computed their minimum possible energy.
2
4. [Harris 8.13 tweaked] Concisely state why the Periodic Table of the
Elements is, in fact, periodic.
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Physics 322: Modern Physics
Spring 2015
5. Using an energy level diagram such as the one
shown here (yours can be hand drawn),
explain why we might expect Neon-20 to be
more tightly bound than Fluorine-20.
Clearly explain the criteria you used to add
neutrons and protons to the figure.
6. Explain to a first year physics major how if we
fuse four hydrogen atoms (each with mass
1.0079u) we can end up with one helium atom
of mass 4.00260u which is less than 4 times
1.00794u = 4.03176u. HINT: In a nuclear
physics perspective, mass is not viewed as a
measure of inertia alone, but instead as a
measure of internal energy. Why does this
matter?
7. Imagine you have an ingot of pure gold. NOTE: The kind of gold bar
traded between banks has a weight of 400 troy ounces (12.4 kg) and has a
value of $480,980 as of April 9, 2015.
a. Estimate the volume of a single gold nucleus assuming it is all the
most stable isotope, 197Au.
b. The mean density of gold is 19300 kg/m3. What fraction of the
space in the ingot is actually gold nuclei you paid for and what
fraction is “empty space?”
c. You decide to fire α particles (helium nuclei) at your gold bar. What
speed would you need to fire the α particles in order to expect some
of them to touch the gold nuclei (ignore quantum tunneling as a
possibility)? Do you have to worry about relativity?
8. Let’s consider a little bit of nuclear fusion that goes on in massive stars
called the triple-α process in which three helium-4 nuclei are fused into
one carbon-12 nucleus.
a. Calculate the binding energy per nucleon for helium-4.
b. Calculate the binding energy per nucleon of carbon-12.
c. What is the implication of these results with regards to the
energetics of the triple-α fusion process?
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