QJEEM12Ph93f6: JEE Main 2012 Physics - Class 12 JEEM12Ph93f6 Solution: A diatomic molecule is made of two masses and which are…

Question

Verified Solution • 2025–26 Session moderate

A diatomic molecule is made of two masses

{m_1}

and

{m_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: (

n

is an integer)

Accepted Answer

The energy of the system of two atoms of diatomic

molecule

E = {1 \over 2}I\omega

where

I=

moment of inertia

\omega =

Angular velocity

= {L \over I}.

L=

Angular momentum

I = {1 \over 2}\left( {{m_1}{r_1}^2 + {m^2}{r_2}^2} \right)

Thus,

E = {1 \over 2}\left( {{m_1}{r_1}^2 + m{}_2{r_2}^2} \right){\omega ^2}\,\,\,\,\,\,\,\,\,...\left( i \right)

E = {1 \over 2}\left( {{m_1}{r_1}^2 + {m_2}{r_2}^2} \right){{{L^2}} \over {{I^2}}}

L = n{{nh} \over {2n}}

(According Bohr's Hypothesis)

E = {1 \over 2}\left( {{m_1}{r_1}^2 + {m_2}{r_2}^2} \right){{{L^2}} \over {{{\left( {{m_1}{r_1}^2 + {m_2}{r_2}^2} \right)}^2}}}

E = {1 \over 2}{{{L^2}} \over {\left( {{m_1}{r_1}^2 + {m_2}{r_2}^2} \right)}}

= {{{n^2}{h^2}} \over {8{\pi ^2}\left( {{m_1}{r_1}^2 + {m_2}{r_2}^2} \right)}}

E = {{\left( {{m_1} + {m_2}} \right){n^2}{h^2}} \over {8{\pi ^2}{r^2}{m_1}{m_2}}}

\left[ {\,\,} \right.

as

\left. {\,\,\,{r_1} = {{{m_2}r} \over {{m_1} + {m_2}}};\,{r_2} = {{{m_2}r} \over {{m_1} + {m_2}}}\,\,} \right]

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