Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Physics

(c) When T # 0,

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n= 1

That is to say, because of thermal excitation (no matter how low the tem-
perature is, provided T # 0), the electrons cannot be bounded by the
nuclei.

(d) The divergence has its origin in the large degeneracy of hydrogen’s
highly excited states. If we confine the hydrogen molecule in a box of
volume L3, these highly excited states no longer exist and there will be no
divergence.

2046

The average kinetic energy of the hydrogen atoms in a certain stellar

(a) What is the temperature of the atmosphere in Kelvins?

(b) What is the ratio of the number of atoms in the second excited

(c) Discuss qualitatively the number of ionized atoms. Is it likely to

atmosphere (assumed to be in thermal equilibrium) is 1.0 eV.

state (n = 3) to the number in the ground state?

be much greater than or much less than the number in n = 3? Why?

Solution:

( wisco nsin)

(a) The temperature of the stellar atmosphere is

zE 2 x 1.6 x 10-19

T=-= = 7.7 x lo3 K.

3k 3 x 1.38 x

(b) The energy levels for hydrogen atom are

En= (-;;.-) -13.6 ev.

Using the Boltzmann distribution, we get