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Question:

A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum, its energy will be given by (n is an integer)

n2h22(m1+m2)r2

2n2h2(m1+m2)r2

(m1+m2)n2h22m1m2r2

(m1+m2)2n2h22m21m22r2

Solution:

r1=m2/(m1+m2)r
r2=m1/(m1+m2)r
(I1+I2)ω=nh/2π
KE=1/2(I1+I2)ω2=(m1+m2)n2h2/2m1m2r2