Vibrational energy level of a diatomic molecule is given by,
$$ E_v = ( v + \frac{1}{2} ) \hbar \omega_0 $$
Where, v=0,1,2,3…. is the vibrational quantum number, \(\omega_0 = \sqrt \frac{k}{\mu} \) , \( \mu \) is the reduced mass of the diatomic molecule and k is the force constant.
The selection rule for transition between vibrational states is,
$$ \Delta v= \pm 1 $$