Photoluminescence excitation spectroscopy was employed to investigate the electronic structure of ZnSe/ZnS core/shell quantum dots. Four excited states viz. 1S(e)-1S(3/2)(h), 1S(e)-1S(e)-2S(3/2)(h), 1P(e)-1P(3/2)(h), and 1S(e)-1S(SO) are observed in ZnSe and ZnSe/ZnS core/shell quantum dots. The experimentally observed excited states for ZnSe/ZnS quantum dots are analyzed on the basis of reported "effective mass approximation" calculations. The photoluminescence quantum efficiency increased from 2% for ZnSe quantum dots to 42% for ZnSe/ZnS quantum dots. X-ray photoelectron spectroscopic and transmission electron microscopic investigations suggest formation of uniform ZnS shell on ZnSe. The electron energy levels of ZnSe/ZnS core/shell quantum dots are investigated as a function of core diameter and ZnS shell thickness, and are compared with bare ZnSe quantum dots. Seven different sizes (ranging between 20 to 52 angstrom) are probed using size-selective photoluminescence excitation technique. Upon building a shell of ZnS on ZnSe quantum dots, the transition from three hole states (1S(3/2)(h), 2S(3/2)(h), 1S(SO)) to 1S(e) remain well defined and have negligible relative shift, suggesting that the valence-band offset is larger than the energy of these states. With increasing ZnS shell thickness, an observed increase in the transition probability of 1S(e)-2S(3/2)(h) state is due to modification of hole states caused by ZnS shell. The relative shift of the P exciton peak (1P(e)-1P(3/2)(h)) with increase in shell thickness is due to a loss of confinement energy of P electron state. The energy of 1P(e)-1P(3/2)(h) is found to be remarkably independent as a function of core diameter.