Using the first-order perturbation theory and exciton-spin-orbit-photon-molecular-vibration-interaction (ESOPMVI) operator, the rates of reverse intersystem crossing (RISC) and thermally activated delayed fluorescence (TADF) are derived. It is shown that the pre-exponential factor of the rate of TADF is not an absolute constant as is commonly assumed. Instead, it depends on the square of the atomic number and the exchange energy, but it also depends on the triplet excitonic Bohr radius as at-6, which enhances the rate of RISC by 4-6 orders of magnitude higher than the rate of the intersystem crossing, which undermines the dependence of the rate on the atomic number, and hence TADF can occur efficiently in metal-free organic solids. This provides a clearer understanding of the mechanism of TADF in metal-free organic light-emitting diodes as has been found recently experimentally.