The number of vacant orbitals present in the valence shell of silicon and zinc are
 

${}_{14}\mathrm{Si};1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3{\mathrm{p}}^2$

valency shell of Si = 3 

third shellcosists of s,p,d orbitals.vacant orbitals = 1+5=6

${}_{30}\mathrm{Zn};1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3{\mathrm{p}}^{6}3{\mathrm{d}}^{10}4{\mathrm{s}}^2$

valency shell = 4 

orbitals 4s,4p,4d,and 4f

vacant orbitals = 3+5+7=15