Answer:
The first ionisation enthalpy of
sodium is lower than that of magnesium as in both the atoms, the electron is to
be removed from 3s-orbital but in sodium the nuclear attraction is less than
magnesium as atomic number of sodium is 11 and that of magnesium is 12 (or
atomic radius of Na is more than atomic radius of Mg).
After the removal of one
electron from each atom, the ions are formed.
\[Na:1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{1}};\] \[N{{a}^{+}}:1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}\]
\[Mg:1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}};\] \[M{{g}^{+}}:1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{1}};\]
Sodium ion acquires the
configuration of an inert gas which is a stable configuration, i.e., all the 2p-orbitals
are completely filled. It is difficult to remove the second electron from this
ion as it requires very high energy, i.e., second ionisation energy is very
high. In the magnesium ion, the second electron is to be removed from 3s-orbital
which is bit easier. Thus, second ionisation enthalpy of Na is much higher than
the second ionisation energy of Mg.
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