Summary form only given. The physical nature of photoluminescence (PL) from semiconductor nanocrystals has been a subject of considerable debate. Earlier studies using organically-capped nanocrystals have shown that the PL arises primarily from dark excitonic states with a radiative lifetime of order microseconds. Recent advances in developing inorganically-capped nanocrystals have led to much improved quantum efficiency and thus prompted the need to reexamine radiative processes in these core/shell nanocrystals. Time-resolved PL of typical core/shell nanocrystals, however, is characterized by complex multi-exponential decays. It has been difficult to extract information on radiative processes from these measurements. We report studies of radiative recombination in core/shell nanocrystals using an experimental approach based on cavity QED and the fact that only radiative processes are affected by modifications in vacuum fluctuations. We single out radiative processes from the complex decay dynamics in time resolved PL by embedding nanocrystals in an optical microresonator and by comparing time-resolved PL obtained at energies resonant or off-resonant with relevant resonator modes. An estimated radiative lifetime of order l0 ns is obtained, indicating that a significant part of the PL arises from dipole-allowed radiative recombination in nanocrystals. Core/shell CdSe/ZnS nanocrystals with a diameter near 5 nm are fabricated by using high temperature organometallic synthesis.