Question

16. Consider a pure hydrogen gas at a temperature of 10,080 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 10.2 eV between these two states. At what temperature would both levels have equal populations?

Answer 1

This is answer of question number 16.

Solution=18 he population in any saved is proportional to - E/KT Nm & In e is degeneracy of lovel level EIKT where in is level. . gn En is energy of k= Boltzmann consdanut For relative populalion T= temperature - (En-En)/KT K= 1.38X10 TK] In e [ k= Nn en 2m2 For Hydrogen , degenerary of devel mis and En' - En = 10.2 eu n = 1; n = 2 En' - En = 1.634 1 10 T T= 100bok 8 N, No exp 11.634 x 10 1.38X10 -23% 10080 0.00003166 NA Now , Por a temperature at which booth devels have equal population N & exp Na 1.634810 1.38x10 e fa In[t] -18 1.634X10 1.38×10 - 23XT T = 85001 k