Question

A nitrogen molecule has two nitrogen atoms separated by a distance of $1.3\times {10}^{-10}$m.

(1)Find its moment of inertia about the centre of mass.

(2)If it's rotational kinetic energy is $4\times {10}^{-21}$, then compute its frequency about the centre of mass.

(Mass of nitrogen atom is $14$ amu).

Answer 1

Moment of inertia of two nitrogen molecules is given by

$I=m{\left(\frac{r}{2}\right)}^2+m{\left(\frac{r}{2}\right)}^2$

$I=\frac{m{r}^2}{2}$

$I=1.96\times {10}^{-46}kg{m}^2$

now for the energy

$K=\frac{1}{2}I{\omega }^2$

$4\times {10}^{-21}=\frac{1}{2}\times 1.96\times {10}^{-46}\times 4{\pi }^2\times f^2$

$f=1.01\times {10}^{12}Hz$