1. A free electron has wave function

(x; t) = sin(kx -wt)

Determine the electron's de Broglie wavelength, momentum, kinetic energy and speed when k = 50nm????1.

Determine the electron's de Broglie wavelength, momentum, total energy, kinetic energy and speed when

k = 50 pm????1.

2. A proton is conned in an innite square well of width 10 fm. (The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by an innite square well potential.) Calculate the energy and wavelength of the photon emitted when the proton undergoes a transition from the rst excited state (n = 2) to the ground state (n = 1). In what region of the electromagnetic spectrum does this wavelength belong?

3. A particle with mass m is in an innite square well potential with walls at x = -L=2 and x = L=2. Write the wave functions for the states n = 1, n = 2 and n = 3.

4. A 1.00 g marble is constrained to roll inside a tube of length L = 1:00cm. The tube is capped at both ends. Modelling this as a one-dimensional innite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. Calculate the exitation energy required to promote the marble to the next available energy state.