Probset 3 part 2

#2. (a) A non-relativistic free particle with mass m has kinetic energy K. Derive an expression
for the de Boglie wavelength of the particle in terms of m and K. (b) What is the de Broglie
wavelength of an 800-eV electron?

#3. An electron in a 1-D infinite well has a ground state energy of 1 eV. (a) What is the length
of the well?

#4. (a) Find the energy difference between the ground state and the third excited state of an
electron confined to a 1-D box with a width of 0.125 nm. (b) An electron initially in the
ground state absorbs a photon which excites it to the n = 4 state. Calculate the wavelength
of this photon.

#5. A hydrogen atom undergoes a transition from the n = 5 to the n = 2 state. (a) What are the
energy and wavelength of the photon that is emitted, and which part of the electromagnetic
spectrum does this photon correspond to? (b) If the angular momentum is conserved and if
the Bohr model is used to describe the atom, what is the angular momentum of the photon?
(Note that the full quantum-mechanical description gives a different result.) [Permittivity
of free space epsilon = 8.854 × 10−12 F m−1.]

Phys 104 prob set 3

1. Muonic atom: A muonic atom consists of a μ-meson (a "heavy electron" of mass mμ) bound
to a positive nucleus. For a nucleus with a small charge (as in muonic hydrogen) the muon orbits
outside the nucleus. However, if the nucleus has a sufficiently large positive charge the muon
actually orbits inside the nucleus! Inside the nucleus the muon feels a nuclear force rather than
the Coulomb force. Assume the nuclear force can be described by

F = –D r , where r is the radius of the muon orbit and D is a constant (note that this is a generalized "spring" force). The force is directed along the radius (i.e. Use the Bohr quantization rule for angular momentum to show that the energy levels for the allowed orbits are given by En = nh(D/mμ )1/ 2.

2. more to come