Download PHYS 221: Homework Assignment 3 This homework due just prior

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PHYS 221: Homework Assignment 3
This homework due just prior to Lecture:
3:20 PM, Monday, February 6, 2017
Reading assignment:
Modern Physics by Harris as follows:
• Read Chapter 5 before the next lecture on Monday. Sections 1, 2, 3, skim 4, 5 (very
important), 6, skim 7, 8, skim 9, skip 10.
Important note: You must show your work. The correct answer alone is worth nothing.
This is absolutely and critically important. I have instructed the graders to ignore answers
that are not explained.
Please hand in your homework on stapled 8 12 × 11 sheets. Please write your name
on the top sheet. Explain your work. Write down the source of any equations you
might use and tell us why you chose to use them. Use the correct physical units
and report your answer with an appropriate number of significant digits. Your final
answer should have a box drawn around it and should be in the form of a sentence if
possible. Neatness counts.
Problem 1: Harris, Problem 5.28 [12 points]
Problem 2: Harris, Problem 5.52 [12 points]
Problem 3: [12 points] An infinitely deep square well has an infinite number of bound
states, but a well of finite depth does not. Roughly how many bound states would you
expect to find in a well of width L and whose depth U1 is large but not infinite?
Homework Assignment continues on the next page....
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Problem 4: [12 points] An electron is Bragg reflected twice. First, it strikes a crystal
surface at an angle θ, and then after being reflected it strikes a second, different crystal, also
at the same angle θ. The spacing between atomic layers in the first crystal is a, and that in
the second crystal is exactly 0.6 a.
a) [6 points] What is the greatest possible value that the wavelength λ of the electron could
have and still be consistent with these facts? [Give your answer in terms of the given fixed
quantities a and θ]
b) [2 points] Now suppose that the electron is replaced by a photon having the same wavelength as the electron had. Will it in general be Bragg reflected or not? If not, why not?
c) [2 points] Now suppose that the electron is replaced by a photon having the same momentum as the electron had. Will it in general be Bragg reflected or not? If not, why
not?
d) [2 points] Now suppose that the electron is replaced by a photon having the same energy
as the electron had. Will it in general be Bragg reflected or not? If not, why not?
Problem 5: [12 points] In the Bohr model of hydrogen-like atoms, an electron of mass m
is in a circular orbit of radius r moving with speed v.
a) [4 points] What does the Bohr postulate say about the relationship between r and v?
b) [8 points] In the Bohr model, the energy levels of a one-electron atom are given by
En = −
h̄2 Z 2
2ma20 n2
A hydrogen atom makes a transition from n = 3 to n = 2 and emits a photon. This photon
strikes a doubly ionized lithium atom, which consists of a single electron and a nucleus
containing three protons, and completely removes the electron. For this to happen, the
lithium ion must be in an excited state.
What is the least quantum number possible, nmin , for this excited state if this process is
to occur?