Question

The energy of a transition from the / = 2 to the / = 3 state in CO is 1.43 x 10^-3 eV. (a) Compute the rotational inertia of the CO molecule. (b) What is the average separation between the centers of the C and O atoms?

Answer 1

a)

$$E=1.43\cdot10^{-3}eV=2.3\cdot10^{-22}J$$

$$I=\frac{n(n+1)h}{8\pi^2kc}=\frac{n(n+1)h^2}{8\pi^2E}$$

$$I=\frac{2(2+1)(663\cdot10^{-34})^2}{8\pi^2(2.3\cdot10^{-22})}=1.45\cdot10^{-46}kg\cdot m^2$$

b)

$$r=\sqrt{\frac{I}{m_a}}=\sqrt{\frac{I(m_c+m_0)}{m_cm_0}}$$

$$r=\sqrt{\frac{1.45\cdot10^{-46}(1.994+2.656)}{(1.994)(2.656)\cdot10^{-26}}}=1.13\cdot10^{-10}m$$