ProblemSet1

# ProblemSet1 - Ch21a Fall 2009  Problem Set 1 ...

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Unformatted text preview: Ch21a Fall 2009  Problem Set 1  TA: Sigrid Barklund  Due: October 14, 2009 at 1pm    Collaboration with other students, notes from this year, and quantum mechanics textbooks  are encouraged, but the answers you turn in must be your own work. Use of solutions  manuals, problem sets from previous years, and internet resources are not allowed. Please  note how much time you spend working this problem set when you turn it in.    1. Blackbody Radiation.   Find the wavelength corresponding to the maximum in the Planck distribution for a  given temperature, and show that the expression reduces to the Wien displacement  law at short wavelengths. Determine an expression for the constant in the law in  terms of fundamental constants. (This constant is called the second radiation  constant.)    2. Photoelectric Effect.  The work function of platinum is 5.65 eV (To what physical property does this  correspond?) What is the minimum frequency of light required to observe the  photoelectric effect on Pt? If light with a 150 nm wavelength is absorbed by the  surface, calculate the kinetic energy and de Broglie wavelength of the emitted  electrons.    3. Particle­Wave Duality.  In an electron diffraction experiment, a monoenergetic beam of electrons is  elastically scattered from a Ni crystal face into a detector at an angle θ. The electron  beam is normal to the surface, and θ is the angle between the incident electron beam  and the scattered electrons.    a) If the crystal lattice is a regular simple cubic array of atoms with a nearest  neighbor spacing of d, and the electrons are of sufficiently low energy that  penetration of the electrons in the crystal is negligible, derive an expression  describing the observed diffraction pattern.  b) It was found experimentally that for electrons of energy 54.0 eV, the most  intense diffraction peak appears at 50.1°. What is the Ni lattice spacing, d?      4. Mathematical Tools for Quantum Mechanics.  For each of the following operators, state whether it is linear and whether it is  Hermitian. Justify your answers.  a Af x d dx x3 fx b Bf x d2 dx2 x fx c Cf x 0 f x' exp x2 fx d dx x' 2 d Df x e Ef x d dx x2 f x    ...
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