ES 485-2, Fall 2015
HW 6
Please note: Homework solutions must be written clearly and explained thoroughly. Diagrams must be
drawn with care and using a ruler or an appropriate drawing application, and to the scale!
Use MATLAB for the linear and surface plots in the following problems!
1. The radius of a hydrogen nucleus is believed to be about r = 1.2 x 10-15 m. (a) What is the
classical speed of an electron moving around a proton at that radius? (b) What is the
total mechanical energy of the electron? (c) Are the results of parts (a) and (b)
reasonable?
2. Use the uncertainty principle to find the bandwidth of Δω of a radar amplifier if it
amplifies a pulse of width 1 μs.
3. Plot the classical Maxwell-Boltzmann velocity distribution F(v) vs. v for the following
temperatures:
a. T = 77 ̊K
b. T = 300 ̊K
c. T = 400 ̊K
4. Create a surface plot of the classical Maxwell-Boltzmann velocity distribution F(v,T).
5. Assume an electron gas with a concentration of 1.24x1028 m-3.
(a) Calculate the Fermi energy EF for this Fermi gas.
(b) Using the Fermi energy obtained in part (a), plot the F-D distribution for the
probability of occupation of states of energy E: Plot FFD (E) vs. E for the following
temperatures:
(i)
T = 77 ̊K
(ii)
T = 300 ̊K
(iii) T = 400 ̊K
(c) Create a surface plot of FFD (E,T).
(d) Calculate the number of electrons in the gas with energies within 0 ≤ E ≤ EF at room
temperature (T=300 ̊K).