Question

why the first ionisation enthalpy of sodium is lower than that of magnesium but it's second ionization enthalpy is higher than that of magnesium​

Answer 1

Explanation:

valence she'll of na has 3s1 so it is easy to lose e hence less IP is required whereas mg has 3s2 so difficult to lose $ more IP

in 2nd IP na has 2p6 so very difficult to lose e due to fully filled stability so high up. whereas mg has 3s1 so easy to lose hence less IP required.

hope you understand the explanation

Answer 2

Electronic configuration of Na and Mg are
Na = 1s2 2s2 2p6 3s1
Mg = 1s2 2s2 2p6 3s2

First electron in both cases has to be removed from 3s-orbital but the nuclear charge of Na (+ 11) is lower than that of Mg (+ 12) therefore first ionization energy of sodium is lower than that of magnesium.

After the loss of first electron, the electronic configuration of
Na+ = 1s2 2s2 2p6
Mg+ = 1s2 2s2 2p6 3s1

Here electron is to be removed from inert (neon) gas configuration which is very stable and hence removal of second electron requires more energy in comparison to Mg.
Therefore, second ionization enthalpy of sodium is higher than that of magnesium.