If a rigid body has moment of inertia I and angular velocity , its kinetic energy is
Question:
If a rigid body has moment of inertia I and angular velocity ω, its kinetic energy is
where L is the angular momentum. The solution of the Schrödinger equation for this problem leads to quantized energy values given by
(a) Make an energy-level diagram of these energies, and indicate the transitions that obey the selection rule Δℓ = ±1.
(b) Show that the allowed transition energies are E1, 2E1, 3E1, 4E1, etc., where E1 = ћ2/I.
(c) The moment of inertia of the H2 molecule is I = 1/2 mpr 2, where mp is the mass of the proton and r ≈ 0.074 nm is the distance between the protons. Find the energy of the first excited state ℓ = 1 for H2, assuming it is a rigid rotor.
(d) What is the wavelength of the radiation emitted in the transition ℓ = 1 to ℓ = 0 for the H2 molecule?
Step by Step Answer:
a b The values of 0 1 2 yield all the po...View the full answer
