A hypothetical ion of an element has a degeneracy equal to 4pi^2, where n is the...
A hypothetical ion of an element has a degeneracy equal to 4pi^2, where n is the principal quantum number. At T=40000 K, the ratio of the number density in level n = 3 to that of the fundamental (n=1) is 0.25. Find the energy of level n=3 assuming E1=0. The answer is 12.34 eV. I have no idea. Please help1 thanks
Homework Answers
From the Boltzmann equation
n1/n3 = (g1/g3)e^([E3-E1]/kT) = 1/0.25
we know g1/g3 = (2*1^2)/(2*3^2) = 2/18
So
( 2/18) e^[E3/(1.38e-23*40000)] = 4
e^[E3/(1.38e-23*40000)]=36
E3 = (1.38e-23*40000)*ln 36
= 1.978e-18 J
= 1.978e-18/1.6e-19 eV
= 12.34 eV
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