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 quantization, its energy will be given by : (n is an integer)

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Physics

Bohrs Model of Atom

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 quantization, its energy will be given by : (n is an integer)

$\frac{2 n^{2} h^{2}}{(m_{1} + m_{2}) r^{2}}$

$\frac{n^{2} h^{2}}{2 (m_{1} + m_{2}) r^{2}}$

$\frac{(m_{1} + m_{2}) n^{2} h^{2}}{2 m_{1} m_{2} r^{2}}$

$\frac{{(m_{1} + m_{2})}^{2} n^{2} h^{2}}{2 m_{1}^{2} m_{2}^{2} r^{2}}$

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$Iω = n ℏ$

Rotational energy $= \frac{1}{2} {Iω}^{2}$ where I = µr²

Putting we get ^{$E = \frac{n^{2} ℏ (m_{1} + m_{2})}{2 m_{1} m_{2} r^{2}}$}