By using Mori memory function formalism we have derived a simple relat
ion for the mass dependence of self-diffusion of a particle in an isot
opic fluid. It has been shown that the Self-diffusion coefficient of a
massive particle for a very large mass ratio (greater than or equal t
o 25) has a unique value at a given density and temperature which is 1
/root 2 times the self-diffusion coefficient of the fluid. The predict
ion of the formula has been supported by the recent molecular dynamics
data on Lennard-Jones fluids. We have also studied the effect of dens
ity and temperature on the mass-dependent self-diffusion coefficient.
It is found that the ratio of self-diffusion coefficient of the heavy
particle to that of the fluid is weakly dependent on thermodynamic sta
te of the fluid.