Physics 5337 - Homework #5

  1. In a system, the period of oscillation T is related to the wavenumber k by

    T [a * k * tanh(b*k)]1/2 = 2 π

    where a and b are constants.

    1. What is the group velocity?
    2. What is the phase velocity?
    3. What is the speed of sound (long wavelength limit)?
    4. If T, a, and b are all equal to 1, what is k?

    1. What is the de Broglie wavelength of a neutron moving at 2000 m/s?
    2. What is its kinetic energy?
    3. What is the de Broglie wavelength of an electron moving at 2000 m/s?
    4. What is its kinetic energy?
    5. Which is more likely to Bragg scatter from a crystal of NaCl?
    6. What energy X-ray has the same wavelength as the particle above that scatters from NaCl?