In 
a 
certain 
kind 
of 
star 
there 
are 
regions 
in 
which 
one 
hydrogen 
atom
 per
 million
 is
.....

In 
a 
certain 
kind 
of 
star 
there 
are 
regions 
in 
which 
one 
hydrogen 
atom
 per
 million
 is
 
in 
the 
first
 excited
 state
(n
=2).
The 
other 
atoms 
can
 be 
assumed 
to

be
 in
 the
 ground
 state
 (n
 =1).
 
 Use
 this
 information
 to
 estimate
 the

temperature 
there.

use the boltzmann equation:

P(n=2)/P(n=1) = g(n=2)/g(n=1) x Exp[(E1-E2)/kT]

where the P's are the populations of electrons in n=2, n=1
g's are the statistical weights = 2n^2 E1 and E2 are the energy levels of the n=1 and n=2 state

for n=2, g=8, for n=1 g=2

the energy spacing between n=1 and n=2 is 3/4 of 13.6 eV = -1.63x10^-18J

so we have

P2/P1 = 8/2 * Exp[-1.63x10^-18/1.38x10^-23 T]

P2/P1 = 10^-6 = 4 Exp[-118,260/T]

solve for T: T=7780K