Example 1.1  

A metal has a workfunction of 4.3 V. What is the minimum photon energy in Joule to emit an electron from this metal through the photo-electric effect? What are the photon frequency in Terahertz and the photon wavelength in micrometer? What is the corresponding photon momentum? What is the velocity of a free electron with the same momentum?

Example 1.2  

The spectral density of the sun peaks at a wavelength of 900 nm. If the sun behaves as a black body, what is the temperature of the sun?

Example 1.3  

An electron is confined to a 1 micron thin layer of silicon. Assuming that the semiconductor can be adequately described by a one-dimensional quantum well with infinite walls, calculate the lowest possible energy within the material in units of electron volt. If the energy is interpreted as the kinetic energy of the electron, what is the corresponding electron velocity? (The effective mass of electrons in silicon is 0.26 m₀, where m₀ = 9.11 x 10^-31 kg is the free electron rest mass).

Example 1.4  

Consider an infinitely long cylinder with charge density r, dielectric constant e₀ and radius r₀. What is the electric field in and around the cylinder?

Example 1.5  

Calculate the energy relative to the Fermi energy for which the Fermi function equals 5%. Write the answer in units of kT.