An investigation of how electron/photon beam exposures affect the intercalation rate of Na deposited on graphene prepared on Si-face SiC is presented. Focused radiation from a storage ring is used for soft X-ray exposures while the electron beam in a low energy electron microscope is utilized for electron exposures. The microscopy and core level spectroscopy data presented clearly show that the effect of soft X-ray exposure is significantly greater than of electron exposure, i.e., it produces a greater increase in the intercalation rate of Na. Heat transfer from the photoelectrons generated during soft X-ray exposure and by the electrons penetrating the sample during electron beam exposure is suggested to increase the local surface temperature and thus the intercalation rate. The estimated electron flux density is 50 times greater for soft X-ray exposure compared to electron exposure, which explains the larger increase in the intercalation rate from soft X-ray exposure. Effects occurring with time only at room temperature are found to be fairly slow, but detectable. The graphene quality, i.e., domain/grain size and homogeneity, was also observed to be an important factor since exposure-induced effects occurred more rapidly on a graphene sample prepared in situ compared to on a furnace grown sample.