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.]