An H₂ in its ground electronic, vibrational, and rotational state absorbs a photon of frequency 1.356 x 10¹⁴ Hz, undergoing a transition to the v = 1, ℓ = 1 state while remaining in the electronic ground state. It then undergoes a transition to the v = 0, ℓ = 2 state, emitting a photon of frequency 1.246 x 10¹⁴ Hz.

(a) Compute the moment of inertia of the H₂ molecule about an axis through the center of mass.

(b) Determine the vibrational frequency and r₀ for H₂ and compare these with the values in Table 9-8.

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Table 9-8 Rotational and vibrational constants for selected diatomic molecules Molecule H₂ Liz 0₂ LiH H³5Cl Na ³5C1 K35Cl K7⁹Br Equilibrium separation r, (nm) 0.074 0.267 0.121 0.160 0.127 0.251 0.279 0.294 Frequency f (Hz) 1.32 × 10¹4 1.05 × 10¹3 4.74 × 10¹3 4.22 x 10¹3 8.97 × 1013 1.14 × 10¹3 8.40 × 10¹2 6.93 X 10¹2 Eor (ev) 7.56 × 10-3 8.39 x 10-5 1.78 x 104 9.27 x 10-4 1.32 x 10-3 2.36 x 10-5 1.43 x 10-5 9.1 x 10-6