I have just read that we are able to estimate the temperature of the earth thousands of years ago by measuring the ratio of certain isotopes present in ice cores that froze thousands of years ago. My understanding of this idea is that $\mathrm{H_2O}$ molecules containing lighter isotopes (i.e. with $\mathrm{^{16}O}$) evaporate quicker than those molecules that contain heavier isotopes (i.e. with $\mathrm{^{18}O}$) and that this difference in evaporation rate exhibits a temperature-dependent relationship.
My problem is that the equipartition theorem says that each molecule should contain an energy of $\frac{1}{2}kT$ per degree of freedom regardless of the molecular mass. If we assume that all the liquid $\mathrm{H_2O}$ molecules roughly obey a Maxwell-Boltzmann distribution, then the heavier isotopes will be moving slower than the lighter isotopes (on average at a given temperature) but their greater mass will mean that all isotopes will still possess the same average kinetic energy (in accordance with the equipartition theorem). So if all the water molecules possess the same kinetic energy on average (regardless of the isotopes they contain), why do those molecules with lighter mass preferentially evaporate? I understand that they are moving quicker than their heavier counterparts but the determination of whether a particle escapes a potential well and evaporates is its kinetic energy not its velocity.
In effect, I am asking why the speed of the molecules determines their proclivity to evaporate (to escape the potential well they inhabit due to intermolecular attraction) when it should be their kinetic energy that determines whether they escape their intermolecular potential well or not. If the evaporation rate is determined by kinetic energy (which I think it should be?) as opposed to velocity, then there shouldn't be any difference in the evaporation rates of different water molecules containing different isotopes because they all contain the same kinetic energy on average.