1. A sodium surface is illuminated with 300 nm wavelength light. If the stopping potential is found to be 1.68 V, determine the work function of sodium and cutoff frequency.
2. Electrons accelerated by an electric potential different of 12.75 V are incident on a collection of hydrogen atoms which were at their ground states initially. Upon this interaction, the hydrogen atoms are excited. Determine the possible wavelengths of the light emitted from the excited hydrogens atoms.
3. A 0.100 MeV photon propagating along the positive x-axis collides with a free electron initially at rest on the axis. After the collision, the electron is scattered along the positive x-axis. Determine the scattering angle of the scattered photon with respect to the positive x-axis, the energy of the scattered photon and the kinetic energy of the scattered electron.
4. Consider a particle of mass m moving in a one-dimensional box which has the two walls at x= -l and x = +2l, respectively. The potential energy of the particle in the box is zero. Sketch the wave function and probability density for the particle at the second excited state (n = 3) and determine the probability of finding the particle in between x = 0 and x = +2l. Determine the energy of the particle at the excited state.