The Rotational Energy of the H_2 Molecule

Introduction:
The rotational energy of a diatomic molecule can be determined by considering its moment of inertia and the rotational quantum number J. In the case of the H_2 molecule, the reduced mass and equilibrium internuclear distance are given. We can use these values to calculate the rotational energy in terms of J.

Calculating the Moment of Inertia:
The moment of inertia, I, is a measure of an object's resistance to rotational motion. For a diatomic molecule, it can be calculated using the reduced mass and the distance between the two atoms.

The reduced mass, M, is given as 8.35 * 10^-28 kg. This is calculated as the product of the masses of the two hydrogen atoms divided by their sum: M = (m1 * m2) / (m1 + m2), where m1 and m2 are the masses of the hydrogen atoms.

The equilibrium internuclear distance, R, is given as 0.742 x 10^-10 m.

Using these values, we can calculate the moment of inertia of the H_2 molecule as: I = M * R^2.

Calculating the Rotational Energy:
The rotational energy of a diatomic molecule can be determined using the rotational quantum number, J, and the moment of inertia, I.

The rotational energy is given by the expression: E(J) = J * (J + 1) * (h^2 / 8π^2I), where h is the Planck constant.

Substituting the calculated moment of inertia into the expression, we can determine the rotational energy of the H_2 molecule in terms of J.

Summary:
The rotational energy of the H_2 molecule can be calculated using the reduced mass and equilibrium internuclear distance. By determining the moment of inertia and using the expression for rotational energy, we can express the rotational energy in terms of the rotational quantum number J. The calculated value can provide insights into the rotational behavior of the molecule.