PH004-Applied Physics

1. In a region of space, a particle with mass m and with zero energy has a time-

independent wave function

ᴪ(x) = Axe-x^2/L

where A and L are constants.

Determine the potential energy U(x) of the particle.

2. A proton is conned in an infinite 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 infinite square well potential.) Calculate the energy and

wavelength of the photon emitted when the proton undergoes a transition

from the first excited state (n = 2) to the ground state (n = 1). In what region

of the electromagnetic spectrum does this wavelength belong?

3. Experiments indicate that 13.6 eV is required to separate a hydrogen atom

into a proton and an electron, that is, its total energy is E= -13.6 eV. Find the

orbital radius and velocity of the electron in a hydrogen atom.

4. A positronium atom is a system that consists of a positron and an electron

that orbit each other. Compare the wavelengths of the spectral lines of

positronium with those of ordinary hydrogen.

5. How much more likely is a 1s electron in a hydrogen atom to be at the

distance a0 from the nucleus at the distance a0/2?

6. A Si sample is doped with 1017

As atoms/cm3. What is the equilibrium hole

concentration p0 at 300K? Where is EF relative to Ei?

7. What is the conductivity of an n-type Si crystal that has been doped

uniformly with 1016 cm-3 phosphorus (P) atoms (donors) if the drift

mobility of electrons is about 1350 cm2V

-1s

-1?

8. If a LED material has band gap of 1.2 eV what color of light will it emit?