Elementary Quantum Mechanics

In the photoelectric experiment, green light, with a wavelength of $522\ \mathrm{nm}$ is the longest wavelength radiation that can cause photoemission of electron from a clean sodium surface. Calculate the work function of sodium. If ultraviolet radiation with a wavelength $250\ \mathrm{nm}$ is incident to the sodium surface, what will be the kinetic energy of the photo-emitted electrons?

An electron is confined to an infinite potential well of size $8.5\ \mathrm{nm}$. Calculate the ground state energy of the electron and radian frequency. How this electron can be put to the fourth energy level?

Explain the concept of effective mass in crystal with necessary mathematical expression and diagrams.