Phys 3402, Exam over Ch 12 and 13.

1. Distribution of 3 particles with 6 units of energy.
a. The Maxwell-Boltzmann distribution.
 Energy State 0 1 2 3 4 5 6 Microstates 1 2 0 0 0 0 0 1 3 2 1 1 0 0 0 1 0 6 3 1 0 1 0 1 0 0 6 4 1 0 0 2 0 0 0 3 5 0 2 0 0 1 0 0 3 6 0 0 3 0 0 0 0 1 7 0 1 1 1 0 0 0 6

7 macrostates    microstates  28
 Energy Avg occupationM-B Avg occupationE-B Avg occupation F-D 0 0.75 0.714285714 0.833333333 1 0.642857143 0.571428571 0.666666667 2 0.535714286 0.714285714 0.333333333 3 0.428571429 0.428571429 0.5 4 0.321428571 0.285714286 0.333333333 5 0.214285714 0.142857143 0.166666667 6 0.107142857 0.142857143 0.166666667

b. Einstein-Bose and Fermi-Dirac
There are 7 macrostates for the Einstein-Bose and 6 for Fermi-Dirac. The average populations are shown above.

2. Helium-neon laser
a. Wavelength 632.8 nm, then energy = hc/wavelength = 1240 eV nm/632.8 nm =         1.95954488 eV

b. delta w/w = sqrt(2*k*T/Mc^2)= sqrt(2*8.67E-5*300/18.62E9)=        1.67146E-06

c. For cubic cavity of L=.1m or V= 1E-3 m^2 and w=632.8nm, the number of modes is
Nm=8*pi*V*(delta w/w)/w^3= 8*pi*1E-3*1.67E-6/(632.8E-9)^3=        1.65637E+11 modes

3. Compare water vapor molecule separation of 3 nm and ice at 0.3 nm with DeBroglie wavelength of water molecule.

DeBroglie wavelength = h/p=hc/pc=hc/sqrt(2*KE*mc^2)=hc/sqrt(3*k*T*mc^2)=
DeBroglie wavelength = 1240 eV nm/sqrt(3*8.67E-5 eV/K*273 K*16.77E9 eV) =         0.035933842 nm
So for the gas there is no question, and for the solid the separation is 10x the deBroglie wavelength, so even in ice
the Maxwell-Boltzmann statistics would appear to be valid.