* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PHYS 221: Homework Assignment 3 This homework due just prior
Survey
Document related concepts
Delayed choice quantum eraser wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
James Franck wikipedia , lookup
Renormalization wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Auger electron spectroscopy wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Tight binding wikipedia , lookup
Atomic orbital wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Electron-beam lithography wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Hydrogen atom wikipedia , lookup
Atomic theory wikipedia , lookup
Transcript
1 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.... 2 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?