(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a pure hydrogen hydrogen gas ata tempeature of 10080 K. What is the ratio of the populations of the ground state(n=1) to the first excited state(n=2). Note that the energy difference is 1.634e-18 joules between these two states. At what temperature would both levels have equal populations?

2. Relevant equations

Boltzmann equation: N(B)/N(A)= g(b)/g(a) exp[(E(A)-E(B))/kT

g=2*n^2

3. The attempt at a solution

finding N(B)/N(A) was easy. N(2)/N(1)=2(2)^2/2(1)^2*exp(1.634e-18 joules)/(10080 K)(1.380 *10^-23))= .000031665

I had a difficult time finding the Temperature when both populations are equal. When both populations are equal, does that imply N(a)/N(b) = 1 because N(a)=N(B)?

Now finding the temperature is simple : 1=4 exp(1.634e-18 joules/(T(1.380e-23)) => T= -85411.7 Kelvins.

The only problem is I don't know if I should assume N(B)/N(A) = 1 , just because the temperatures are equal

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# Boltzmann equation problem

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