Domain: Reaction dynamics

In a crossed-molecular-beam experiment investigating the dynamics of the F(^2P_{3/2}) + D2(v=0, j=0) -> DF(v', j') + D reaction at a collision energy of E_coll = 3.2 kcal/mol, the center-of-mass angular distribution of the products is observed to be strongly backward-scattered. The reaction is known to be governed by an early barrier Potential Energy Surface. Estimate the specific rovibrational state (v', j') of the DF product that corresponds to the maximum flux observed in the backward direction. (Constants: D0(D2) = 103.2 kcal/mol, D0(DF) = 136.3 kcal/mol, we(DF) = 2906 cm^-1, Be(DF) = 10.8 cm^-1, M(F) = 19.00 amu, M(D) = 2.014 amu).

Grading rubric:
criterion: The solution correctly determines the numerical value of the exothermicity as 33.1 kcal mol⁻¹.
weight: 10
criterion: The solution correctly determines the total available energy as 36.3 kcal mol⁻¹.
weight: 10
criterion: The solution explicitly applies the skew-angle definition cos²β = (m_A m_C)/[(m_A + m_B)(m_B + m_C)].
weight: 20
criterion: The solution correctly determines β ≈ 47.7°.
weight: 20
criterion: The solution correctly computes the product translational recoil energy as approximately 16.4 kcal mol⁻¹.
weight: 10
criterion: The solution explicitly invokes Polanyi’s rules for an early-barrier surface.
weight: 10
criterion: The solution correctly reports the dominant rovibrational product state as (v′ = 2, j′ = 11).
weight: 20

Answer:
(v' = 2, j' = 11)