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

(N/A) The first ionization enthalpy of $Na$ is lower than that of $Mg$ due to two main reasons:
$1.$ The atomic size of $Na$ $([Ne] 3s^1)$ is larger than that of $Mg$ $([Ne] 3s^2)$.
$2.$ The effective nuclear charge of $Mg$ is higher than that of $Na$.
Consequently,the energy required to remove the first electron from $Mg$ is higher than that for $Na$.
However,the second ionization enthalpy of $Na$ is higher than that of $Mg$. After the loss of the first electron,$Na^+$ attains the stable noble gas configuration $(1s^2 2s^2 2p^6)$. Removing a second electron from this stable configuration requires a very high amount of energy.
In contrast,$Mg^+$ $([Ne] 3s^1)$ still has one electron in the $3s$-orbital. Removing this electron is relatively easier compared to removing an electron from the stable noble gas core of $Na^+$. Therefore,the second ionization enthalpy of $Na$ is significantly higher than that of $Mg$.