Question

The probability of finding a diatomic molecule with vibrational constant ωe=200 cm−1 in the v = 1 vibrational state at a temperature of 300 K is which of the following?

Answer 1

To calculate the probability of finding the diatomic molecule,

probability =

$=exp \left ( \frac{-h\omega v}{2\pi kT} \right ) =exp\left ( \frac{-\omega v}{0.695T}\right )$

w = frequency = 200 cm^-1

v = 1

T = temperature = 300 K

So, probability =

$=exp\left ( \frac{-\omega v}{0.695T}\right ) = exp\left ( \frac{-200\times 1}{0.695\times 300} \right )$

= 0.38

Probability = 0.38 = 38 %