Kinetic Isotope Effect in the Dissociation Reaction CHCl3 → CHCl2(+) + Cl(-)

Question:
In the dissociation reaction

the activated complex resembles the product CHCl₂⁺. For C-H vibration take 800 cm^-1  for the reactant and 1350 cm^-1 for the transition state. At T=298 K calculate the kinetic isotope effect, i.e., k(C − H)/k(C − D).

Solution:
For this first order reaction, when the products are in excited state, the rate constant is given by,

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