The three principal moments of inertia of a methanol (CH3OH) molecule have the property I_x = I_y = I and I_z I. The rotational energy eigenvalues are

hbar ^22Il( l + 1 ) + hbar ^2m_l^22( 1I_z - 1I )

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Atomic and Molecular Physics

The three principal moments of inertia of a methanol (CH₃OH) molecule have the property $${I_x} = {I_y} = I$$ and $${I_z} \ne I.$$ The rotational energy eigenvalues are

A) $$\frac{{{\hbar ^2}}}{{2I}}l\left( {l + 1} \right) + \frac{{{\hbar ^2}m_l^2}}{2}\left( {\frac{1}{{{I_z}}} - \frac{1}{I}} \right)$$ B) $$\frac{{{\hbar ^2}}}{{2I}}l\left( {l + 1} \right)$$ C) $$\frac{{{\hbar ^2}m_l^2}}{2}\left( {\frac{1}{{{I_z}}} - \frac{1}{I}} \right)$$ D) $$\frac{{{\hbar ^2}}}{{2I}}l\left( {l + 1} \right) + \frac{{{\hbar ^2}m_l^2}}{2}\left( {\frac{1}{{{I_z}}} + \frac{1}{I}} \right)$$

Answer & Solution

Correct Answer: Option A

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The three principal moments of inertia of a methanol (CH3OH) molecule have the property $${I_x} = {I_y} = I$$ and $${I_z} \ne I.$$ The rotational energy eigenvalues are

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The three principal moments of inertia of a methanol (CH₃OH) molecule have the property $${I_x} = {I_y} = I$$ and $${I_z} \ne I.$$ The rotational energy eigenvalues are