Molecular rotation: The spacing of the atoms (treated as point masses) in the H₂ molecule is 7.4 × 10^-11 m. What is the energy of the l = 1 rotational level? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, m_h ≈ m_proton = 1.67 × 10^-27 kg) A) 0.090 eV B) 0.070 eV C) 0.045 eV D) 0.030 eV E) 0.015 eV

Question

Quizplus · Accepted Answer

The energy of a rotational level is given by E = l(l+1)ħ²/(2I), where I is the moment of inertia I = μr², and μ is the reduced mass μ = m_h/2 for H₂. Substituting the values, E = 1(1+1)(1.055×10⁻³⁴)²/(2×(1.67×10⁻²⁷/2)×(7.4×10⁻¹¹)²) ≈ 2.4×10⁻²¹ J = 0.015 eV.

Molecular Rotation: the Spacing of the Atoms (Treated as Point