Question

How would you explain the fact that the first ionisation enthalpy of sodium is lower than that of magnesium but its second ionisation enthalpy is higher than that of magnesium?

Answer 1

First ionisation enthalpy of sodium $(Na=1s^2,2s^2,2p^6,3s^1)$ is lower than that of magnesium $(Mg=1s^2,2s^2,2p^6,3s^2)$ because the electron to be removed in both the cases is from 3s - orbital but the nuclear charge is lower in Na than that of magnesium.
After the removal of first electron $N{a}^{+}$ acquires inert gas (Ne) configuration $(N{a}^{+}=1s^2,2s^2,2p^6)$ and hence, removal of second selection from sodium is difficult.
While in case of magnesium after the removal of the first electron the electronic configuration of $M{g}^{+}is1s^2,2s^{2}2p^6,3s^1$ in this case $3s^1$ electron is easy to remove in comparison to remove an electron from the inert gas configuration. Therefore,$I{E}_2$ of Na is higher than that of magnesium.