A particle confined to rotate on a sphere is a very good approximation for the rotations ofdiatomic molecules. Using the equation for the energy of a particle rotating on a sphere, compute the equilibrium bond length of H137I, given that the rotational energy in the`= 5state is 8.952×10−21J. HINT: You will need to use the reduced mass.

the equilibrium bond length of H137I is

Explanation:

The quantum state has a rotational energy which can be expressed mathematically

Here,

               B is the rotational constant given as

      We are given from the question that

   Substituting we have

 Where,

          h is plank constant

          r is radius

          I is moment of inertia  

     Making the subject

  The moment of inertia = Reduced mass ×

            Therefore

Making the subject of the formula