A Diatomic Quantum Mechanical Oscillator Has a Moment of Inertia $7.73 \times 10 ^ { - 45 } \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$

A diatomic quantum mechanical oscillator has a moment of inertia of $7.73 \times 10 ^ { - 45 } \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ . What is the rotational energy when it is in the quantum state characterized by $L = 2$ ? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \right.$ $\left. \mathrm { J } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A) $8.71 \times 10 ^ { - 5 } \mathrm { eV }$
B) $2.27 \times 10 ^ { - 5 } \mathrm { eV }$
C) $2.70 \times 10 ^ { - 5 } \mathrm { eV }$
D) $7.22 \times 10 ^ { - 5 } \mathrm { eV }$