A Sample Problem Using the Boltzmann Equation
Find, at a level in the solar photosphere where T = 5780 K, the ratio of the
number of hydrogen atoms in the first excited state to the number in the
ground state. (Given: For neutral hydrogen the statistical weight of the nth
energy level is gn = 2n2. The first excited state lies 10.15 eV above the
ground state.)
We shall use the subscript i = 1, to represent the ground state and i = 2 to
represent the first excited state. Following this convention the Boltzmann

i
N 2 g 2   2 kT
N i g i e kT
 e
. For

, and, therefore,
equation becomes
N
g
N
u(T )
1
1
hydrogen, g1 = 2, g2 = 8 and χ2 = 10.15 eV. So
N2 8
 e
N1 2
10.15 eV
( 8.6177910 5 eV/K) (5780 K )
 5.65  10 9 
1
.
1.77  10 8