Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Physics 191

For H-, both electrons are in their ground state with total spin 0 (sin-
glet), as the space wave function is symmetric when the particles are inter-
exchanged. Therefore, the spin degrees of freedom of H- correspond only
to the two spin states of the nucleon; hence

The conditions for chemical equilibrium are

so that

Thus, the relative probabilities of finding H+, Ho and H- are

If PH = PH-, or [HO] = [H-I, we have

w=- pe = ---€a + kT In 2 w 0.6 eV.

2030

The potential energy V between the two atoms (m~ = 1.672x g)

in a hydrogen molecule is given by the empirical expression

1.

v = D{e-za(r--ro) - 2e-a(r-r~)

where r is the distance between the atoms.

D = 7 x erg,