Problems and Solutions on Thermodynamics and Statistical Mechanics

214 Pwblema tY Solutions on Thermodynamics 6' Statistical Mechanics

Inserting El = -13.6 eV, E3 = (-13.6/9) eV, and kT = (2/3) eV into the
above, we have N3/N1 M 1.33 x

(c) The number of ionized atoms is the difference between the total
number of atoms and the total number of atoms in bound states, i.e., the
number of atoms in the level n = 00. Obviously, it is much smaller than

the number in n = 3. Thus - Nion = exp ($) M 0.1, i.e., Nion is about

one-tenth of N3.

N3

2047

A monatomic gas consists of atoms with two internal energy levels: a

ground state of degeneracy g1 and a low-lying excited state of degeneracy

92 at an energy E above the ground state. Find the specific heat of this

gas.

(CUSPEA)

Solution:

According to the Boltzmann distribution, the average energy of the

atoms is

where Eo is the dissociation energy of the ground state (we choose the

ground state as the zero point of energy). Thus

2048

Consider a system which has two orbital (single particle) states both

of the same energy. When both orbitals are unoccupied, the energy of the

system is zero; when one orbital or the other is occupied by one particle, the