The rotational absorption spectrum of H³⁵CI shows the following lines

Neglecting centrifugal distortion, the value of the rotational constant in units of cm^-1 is estimated as

Concept:

• The basic quantum mechanical model of rotational spectroscopy is "particle on a sphere" or "the rigid rotor model".
• Rotational spectroscopy deals with a system consisting of two atoms connected by a bond of fixed length (simply a diatomic molecule). It can rotate to describe the entire 3D space resulting in an infinite number of circular trajectories that eventually describe a sphere.
• The rotational energy level for a particular state (Jth state) is given by

, where J is a quantum number (J=0,1,2...) and I is the moment of inertia (, where  is the reduced mass and R is the bond length).

• As 

 let,  

 where B is the rotational constant.

• The energy difference between any two consecutive levels J and J+1 is given by:

• The spectrum depicted below is an absorption spectrum:

• Thus, these spectral lines are equispaced.

Explanation:

• The rotational absorption spectrum of H35CI shows the following lines

• Now, the energy separation of H35Cl rotational energy levels between J"=3 and J" = 4 is 83.03 cm1 and the energy separation of H35Cl rotational energy levels between J"=3 and J" = 4 is 104.10 cm-1
• Thus, the energy separation between rotation spectrum lines 3→4 and 4→5 J" = 9 is 

= 104.10 cm-1 - 83.03 cm1 

= 21.07 cm1 

• The energy separation between the two successive spectral lines is 2B.
• Hence, 

= 10.53 cm^-1​

Conclusion:

Thus, the value of the rotational constant in units of cm-1 is estimated as 10