# Kinetic isotope effect - why transition states taken as isoenergetic I am working on the derivation of the equation below for the difference in activation energies for the two reactions (1) and (2).

I've done the derivation, but I am unsure on some of the approximations I have used. When considering the activation energies I have just used the zero point energy for the C-H and C-D bonds - I am not sure why I can do that, but I assume its because the rest of the zero point energies cancel out.

Secondly I am confused why I can consider the transition states as isoenergetic, as to me they look like they would different energies.

H and D each have 1 electron so the electronic energy can be considered to be the same. In calculating energy of the vibrational quanta then the difference in mass becomes important, as you indicate, via $E = \frac{h}{2\pi}\sqrt{k/\mu} \pu{~~(J/molecule)}$ where k is the force constant, equal for C-H and C-D bonds, and $\mu$ is the reduced mass $m_1m_2/(m_1+m_2)$.