Question 2 Describe all possible distributions of 50 molecul

Describe all possible distributions of 50 molecules with a total energy of Five equal quanta, where the available energy levels have 0, 1, 2, 3, 4, and 5 quanta. Which distribution is most probable. For a certain collection of molecules at equilibrium at 100k the energies of the first Three levels are 0, 3 Times 10^-22 and 5 Times 10^-22 J. The corresponding degeneracies are 1,3 and 5. Find the relative populations of the levels. Calculate the partition function for a system of molecules at 80K in which the Available energies are 0, 1,2 and 3 quanta and the degeneracies are 1,3, 5 and 7 respectively. Each quantum is 5 Times 10^-22 J. An electron gas obeys the Maxwell Boltzman statistics. Calculate the average thermal energy in electron volts of an electron in the system at temperature 300K.

Solution

Since the total energy is 5 quanta, the molecules are distributed as follows.

1 in level 5 and 49 in level 0

5 in level 1 anf 45 in level 0

1 in level 1,1 in level 4 and 48 in level 0

1 in level 2,1 in level 3 and 48 in level 0

The most probable distribution is Boltzmann\'s distribution.