For a rotating molecule with a constant moment of inertia what is the energy difference between the l = 5 and l = 7 energy levels? A)2 E_0r B)24 E_0r C)86 E_0r D)26 E_0r E)35 E_0r

Question

Quizplus · Accepted Answer

The energy levels of a rotating molecule with a constant moment of inertia are given by the formula: E = (l(l+1)h^2)/(2I), where E is the energy, h is Planck's constant, l is the quantum number, and I is the moment of inertia. The energy difference between the l=5 and l=7 energy levels can be calculated as: ΔE = E7 - E5 ΔE = [(7(7+1))/(2I)]h^2 - [(5(5+1))/(2I)]h^2 ΔE = [26h^2/I] Therefore, the energy difference between the l=5 and l=7 energy levels is 26 E_0r. The correct choice is (D).

For a Rotating Molecule with a Constant Moment of Inertia