Modern Physics Final  due 2pm, Wed, Oct 27, 2004   name:_____________________________

 

Honor code:_____________________________

 

You may consult your notes, the textbook, your calculator, an integral table (or integrals.com, etc.), or Patricia or me, but nothing and no one else. Explain all your reasoning and show all your work. When youÕve finished, re-read your work, cross out whatever you no longer believe to be true, and make sure you have answered the questions. Staple your test, in a competent way, with this page on top. If you have any doubt about what is being asked in any of the questions, please ask me about it.

 

  1. (15 points) Some DU students are measuring the photoelectric effect. Their monochromator isnÕt calibrated; they know the wavelength is proportional to the reading on the dial, but they donÕt know what the constant of proportionality is. WeÕd like you to determine whether their data are good, meaning, is the dependence of stopping voltage on wavelength what youÕd expect? Their data are: 

wavelength (arb. units)

100

125

150

175

200

225

stopping voltage (V)

7.7

6.2

5.3

4.1

3.2

2.1

 

 

  1. (20 points) LetÕs return once again to the particle of mass m in an infinite well of width L. At t=0, the wave function is . Directly determine, for all times t, the values of <x>, <p>, and <E>, and show that the results are consistent with each other.

 

  1. (10 points) Suppose we begin with singly-ionized beryllium, that is, a beryllium atom that is missing one electron. Estimate how much energy we must supply to remove another electron from this atom. Is your estimate likely to be high or low?

 

  1. (20 points) Consider a wave function . (a) Does this particle have a well-defined momentum? (b) What is the magnitude of C? (c) What is <x>? (d) What is <p>? (e) IÕm not asking you to calculate Dx, but I do want to know what would happen to its value if the constant b were doubled.

 

  1. (10 points) Consider the function , where b is a real number. The magnitude of this function oscillates sinusoidally between what values and at what angular frequency?

 

  1. (10 points) Suppose a neutron combines with a He-3 nucleus (consisting of two protons and one neutron) to make a normal He nucleus, and a photon is emitted or absorbed in this process. Which is it, absorbed or emitted? What is the wavelength of this photon?

 

  1. (10 points) Prove that  is an eigenfunction of L2 for the right value of n. What is that right value of n?

 

  1. (5 points) The spacings between energy levels for the infinite well are proportional to n, and for a macroscopic object n can be huge! So, why donÕt we notice that a baseball in a shoebox can have only certain kinetic energies?