The allowed rotational energies of a diatomic molecule are given by In this expression l...

The allowed rotational energies of a diatomic molecule are given by

In this expression l is the rotational quantum number and can take the values l = 0, 1, 2 …; I is the rotational inertia of the molecule about an axis through its center of mass; and ℏ= h/2π. The equilibrium separation of the two atoms in a diatomic hydrogen molecule H2 is about 0.074 nm. The mass of each hydrogen atom is about 1.67 × 10−27 kg.

a. Show that the rotational inertia of the hydrogen molecule about an axis through its center of mass is about I =4.6× 10−48 kg · m2.

---

b. Find the difference in energy between the first excited rotational energy stale and the ground rotational state. That is, find . Express the answer in both J and eV.

---

c. Find the relative likelihood Pl = 1/Pl = 0 that a hydrogen molecule will be in its first excited rotational state in thermal equilibrium at room temperature, T = 293 K. (Ignore possible state degeneracies.)