Introduction to High Resolution Spectroscopy 
Introduction Rotational Vibrational Miscellaneous

Rotational Energy Levels For A Rigid-Rotor Diatomic Molecule
  
 

The rotational energy levels (in cm-1) for the rigid-rotor diatomic are given by the formula:

E=BJ(J+1)

J is the rotational quantum number and be zero or any positive integer (0, 1, 2, 3, 4, 5...). B is the rotational constant and is inversely proportional to the moment of inertia of the molecule, I:

B=h/(8*pi^2*c)

where h is Planck's constant (6.626 x 10-34 J s) and c is the speed of light (2.998 x 10-10 cm s-1). The moment of inertia for a diatomic molecule is simply related to the length of the bond (r) and the masses of the two atoms (m1 and m2):

I=mu*r^2
  
where m is the reduced mass, given by
mu=(m1*m2)/(m1+m2)



Input values into the calculator below for the bond length and atomic masses and press "calculate" to work out the energy levels. Alternatively, just enter a value of B to work out the energy levels or B and either the atomic or reduced mass to work out the bond length.

Once you have covered all of the available resources for rotational spectroscopy, you should test your knowledge and understanding with the self test.

Hit the 'Graphical' button to see an interactive graphical version of this calculator.


rigid rotor energy level calculator
 
bond length r (Å) m1 (amu) m2 (amu)



rotational constant (cm-1)
 moment of inertia (kgm2) reduced mass (kg)
       
    J    energy (cm-1)


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