Question

Why is their a discontinuity in values of the ionization enthalpy of aluminium and galium

Answer 1

zeff almost remain same by slater's rule. what happens there are electron repulsions in an atom ( negative negative repel) which we call shielding (shielding of s>p,>d>f).
about the radius of respective atom , as there are many d electrons present in galium which have very poor shielding and hence it explains the radius of gallium,<radius of aliminium
Potential energy = k(Zeff)e/r as zeff almost equivalent and due to radius relationship we can explain your problem