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?

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(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 $Mg$.

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Among the second period elements,the actual ionization enthalpies are in the order $Li < B < Be < C < O < N < F < Ne$. Explain why:
$(i)$ $Be$ has higher $\Delta_{i}H$ than $B$
$(ii)$ $O$ has lower $\Delta_{i}H$ than $N$ and $F$?

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$A$ sudden large jump between the values of second and third ionisation energies of an element would be associated with the electronic configuration:

Consider the following changes:
$M_{(s)} \to M_{(g)}$ ........$(1)$
$M_{(s)} \to M^{2+}_{(g)} + 2e^-$ .......$(2)$
$M_{(g)} \to M^{+}_{(g)} + e^-$ .........$(3)$
$M^{+}_{(g)} \to M^{2+}_{(g)} + e^-$ .........$(4)$
$M_{(g)} \to M^{2+}_{(g)} + 2e^-$ ..........$(5)$
The second ionization energy of $M$ could be calculated from the energy values associated with:

As one moves along a given row in the periodic table,ionization energy

Given below are two statements:
Statement $I$: The decrease in first ionization enthalpy from $B$ to $Al$ is much larger than that from $Al$ to $Ga$.
Statement $II$: The $d$ orbitals in $Ga$ are completely filled.
In the light of the above statements,choose the most appropriate answer from the options given below:

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