You have a vibrational degree of freedom that can be treated like a harmonic oscillator with aspacing between energy levels of 538,03 cm1, What is the probability that this degree of freedom isin state v = 1 at a temperature of 1,138.2 K. Give your answer with at least 3 significant figures.

Probability of a particle indicate the possibility of a particle present in particular vibrational…

Answered: You have a vibrational degree of…

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter14: Rotational And Vibrational Spectroscopy

Section: Chapter Questions

Problem 14.62E

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As noted in lecture, the rigid rotor model can be improved by recognizing that in a realistic anharmonic potential, the bond length increases with the vibrational quantum number v. Thus, the rotational constant depends on v, and it can be shown that By = Be – ae(v +). For 'H®Br, B = 8.473 cm1 and a = 0.226 cm². Use this information to calculate the bond length for HBr a) as a rigid rotor, and b) as a nonrigid rotor in the ground vibrational state. Find a literature value for this bond length (cite your source) and compare your answers. Under what conditions would you expect the nonrigid rotor to be a significantly better model?
Calculate the ratio of the populations in the first two rotational energy levels of carbon monoxide, the lowest J=0 energy level and the higher J = 1 energy level, at 300 K if the energy difference between the levels is 3.8 cm-1and the degeneracies gJ of the two levels are g0 = 1 and g1 = 3, respectively. (You will see in Section 20.3 that there are 2J 1 1 rotational quantum states at each energy level EJ.)
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You have a vibrational degree of freedom that can be treated like a harmonic oscillator with a spacing between energy levels of 538.03 cm1, What is the probability that this degree of freedom is in state v= 1 at a temperature of 1,138.2 K. Give your answer with at least 3 significant figures.