Question

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3.) The lowest two electronic energy levels of the molecule NO are two-fold degenerate and occur at 0 cm1 and 121.1 cm respectively. Determine the probability of occupying one of the higher energy states at 100, 500, and 2000 K

Answer 1

The expression of partition function is as follows: 9=28,em. So, pressure is Here, g, is the degeneracy of the states, & is the energy of the states and his constant Consider the following figure:

-1 Energy/cm 121.1 - - -

Find out the probability of energy level of above energy level diagram at temperature T. There is two states one at ε = () and second at &=121.1 cm-' with degeneracy g, = 2 So, equation (1) becomes, P; = 8,0 Ben 9 - 2x e la p. =- " geli+g₂e Bez (121.1 cm) 2e 0.695 cm-K-'xt (121.1 cm') 2 +2e 0.695 cm KxT At 100K Calculate probability of the higher energy level P = (121.1 cm') 2e 0.695 cm' K 'x100 K (121.1 cm') 2+e 0.695 cm ' K 'x100 K 2e-1.742 2 +2e-1.742 2x0.175 2+2x0.175 = 0.1489 = 0.149 Hence, the calculated value of probability of the higher energy level at 100 K is

At 500 K Calculate probability of the higher energy level Paleo (121.1 cm') 2e 0.695 cm K-'x500 K (121.1 cm ) 2 +2e 0.695 cm K-'x500 K 2e-0,348 2 + 2e-0.348 2x0.706 2 + 2x0.706 = 0.414 Hence, the calculated value of probability of the higher energy level at 500 K is 0.414

At 2000 K Calculate probability of the higher energy level (121.1 cm') 2e 0.695 cm'' K•'2000 K P. =- (121.1 cm') 2+2e 0.695 cm K-"x2000 K 2e-0.087 2 +2e-0.087 2x0.916 2+2x0.916 = 0.478 Hence, the calculated value of probability of the higher energy level at 2000 K is 0.478