1.

A diatomic molecule is made of two masses m_(1)andm_(2) which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by :

Answer»

`((m_(1)+m_(2))N^(2)H^(2))/(2m_(1)m_(2)r^(2))`
`((m_(1)+m_(2))^(2)n^(2)h^(2))/(2m_(1)^(2)m_(2)^(2)r^(2))`
`(n^(2)h^(2))/(2(m_(1)+m_(2))r^(2))`
`(2n^(2)h^(2))/((m_(1)+m_(2))r^(2))`

Solution :`m_(1)r_(1)=m_(2)r_(2)andr_(1)+r_(2)=r`
`because r_(1)=(m_(2)r)/(m_(1)+m_(2))""...(1)`
and `r_(2)=(m_(1)r)/(m_(1)+m_(2))""...(2)`

`E=(1)/(2)Iomega^(2)=(1)/(2)(m_(1)r_(1)^(2)+m_(2)r_(2)^(2))omega^(2)""...(3)`
`because mvr=(nh)/(2pi)=omegaIimpliesomega=(nh)/(2piI)""...(4)`
(put equations (1), (2) and (4) in (3))
we get
`E=((m_(1)+m_(2))n^(2)h^(2))/(2m_(1)m_(2)r^(2))`


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