Question

Physical Chemistry. Please show all your work. I'll rate. Thank you in advance!

15. Given the Boltzmann distribution, e-E/kbt, the probability to find a vibrating particle in the fourth excited state, relative to that for the second excited state, at temperature 300K, is (for w = 1012 Hz.) (a) 0.9035 (b) 0.9505 (c) 0.9750 (d) 1.0000

Answer 1

15. Given that, Boltzmann clistribution, e-Elkos T. Temperature - 300k W = 1012 Hz . To, Find, Vibrating Particle in fourth excited State, relative to that for the second excited State we know, Vibrational array, (n = (142) hu) we, have, n=1,2,3,4,5, 1 sth excited state pencited State... To be found for E4, Ez Ey ; (* + 4) hu (Substituting n=4) 6=1244) hw (substituting n=2) we know, h= 1054x10-34 Substituting hivele hou get De z E4-Ez + (444) hw –(2+2) his - 1 he She

= q hw E4-E2 = 2hu E = zho Relative Ratio = e-EylEBT é -5/gT é (DE) |KBT ( we have DE=E4-E2 Substituting the - Saulk we have KB= 1.38 X10-23 m² kg kl and T= 300 according to giren data Substituting the values, we get KBT = 4.1481021 J Ae . 2 107 10 KBT T14x1021 @-0.0509 - e-0.0509 = 0.9505)