Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Statistical Thermodynamics – General · Exam: CSIR-NET DEC 2014 · Marks: 2 · Difficulty: Medium
The probability of finding the harmonic oscillator in the energy level $n=1$ is (neglect zero point energy and assume $h
u=kBT$)
(a)e
(b)$e^{2}$
(c)$1-e^{2}$
(d)$e^{-2}(e-1)$
Answer
Answer (as printed): D
Explanation
Neglecting zero point energy, $q=\dfrac{1}{1-e^{-h\nu/kT}}=\dfrac{1}{1-e^{-1}}$ (since $h\nu=kT$).Probability $=\dfrac{e^{-\Delta\epsilon/kT}}{q}=\dfrac{e^{-1}}{1-e^{-1}}=e^{-2}(e-1)$.