For a set of nondegrenerate levels with energy ek0100 and 20

For a set of nondegrenerate levels with energy e/k=0,100, and 200K, Calculate the probability of occupyin g each state ehen T=50,500, and 500K. As the temperature continues to increase, the probabilities temperature continues to increase, the probabilities will reach a limiting value. What is this limiting value?

Solution

for T = 50K

E1 = exp(-e/kT) = exp(-0/50) = 1,

E2 = exp(-100/50) = 0.13533,

E3 = exp(-200/50) = 0.0183,

P1(probability of occupying E1 state) = E1/(E1+E2+E3) = 1/(1+0.135335+0.0183) = 1/1.153635

= 0.8668,

P2( for 100K level) = 0.13533/(1.153635) = 0.1173,

P3(for 2oo K level) = (0.0183/1.153635) = 0.015863,

for T = 500 K

E1 = exp(0) = 1,

E2 = exp(-100/500) = 0.8187,

E3 = exp( -200/500) = 0.67,

P1 = 1/(1+0.8187+0.67) =1/ 2.4887 = 0.4,

P2 = 0.8187/2.4887 =0.329,

P3 = ( 0.67/2.4887) = 0.269,

as temp increases max limiting value will reache P = 0.333 ( for 3 energy leve system)