The effects of Zn impurities on the electronic state in the vortex core were investigated systematically in almost optimally doped YBa 2 (Cu 1Àx Zn x ) 3 O y (0 x 0:06) using the microwave complex surface impedance (Z s ) measurement technique. We estimated the viscosity, , and the pinning constant, p , of a vortex as functions of temperature and x on the basis of a mean-field theory of the vortex motion. p as a function of Zn concentration, x, suggests that Zn doping is not an effective procedure for pinning the vortex motion. ðxÞ depended very weakly on x for x 0:003, while it decreased rapidly with increasing x for x > 0:003. These finding suggest that the scattering of QPs in the vortex core is much larger than that in the Meissner (zero-field) state for x 0:003. On the other hand, for x > 0:003, the scattering of QPs in the vortex core is governed by Zn impurity, showing that the presence of the vortex is not important for the scattering in this regime. The large scattering in the low-doping-concentration region (x 0:003) is particularly important, since this is characteristic of the presence of the vortex core. Our result is consistent with the previously published microwave result for the Zn-free material [Tsuchiya et al.: Phys. Rev. B 63 (2001) 184517] in the sense that both experimental data suggest the existence of the high QP-DOS in the vortex core, but is inconsistent with a picture proposed by STM measurements on the vortex core. We discuss possible origins for this discrepancy, including novel mechanisms of energy dissipation in the motion of a moderately clean (' $ ) vortex core.