Question

Which atom that has the largest second ionisation energy?
A. $Mg$
B. $Cl$
C. $S$
D. $Ca$
E. $Na$

Answer 1

The second ionisation energy, unlike the first ionisation energy, is the energy required to remove an electron from the outermost shell of a positive ion, and it is much higher for the metal ions which have a stable octet after the removal of the first ion.
Higher value of second ionisation energy signifies that it is difficult to remove the next electron because of the higher stability of the ion.

Complete step by step answer:
We will first consider the definition of the ionisation energy in order to understand the whole concept. So Ionisation energy is the minimum amount of energy required to remove the most loosely bound electron from the outermost shell, of an isolated neutral gaseous atom or molecule.
Because of increasing distance of the outer electron shell from nucleus as inner shells are added
$X(g)+energy\to {{X}^{+}}(g)+{{e}^{-}}$
Where $X$ is an atom or molecule, ${{X}^{+}}$ is the cation, or the positive ion of that same atom, after losing an electron, which is denoted by ${{e}^{-}}$. This is generally an endothermic process. As a rule, the closer the outermost electrons to the nucleus of an atom, the higher the atom’s ionization energy.
We can do the comparison of ionisation energies of atoms in the periodic table which reveals two periodic trends which are expressed below.
Ionisation energy generally increases from left to right within a given period (that is, row).
Ionisation energy generally decreases from top to bottom in a given group (that is, column).
So we can say that Sodium or the $Na$ atoms have the largest second ionisation energy. When sodium loses one electron, it forms $N{{a}^{+}}$ ion which has the stable noble gas configuration as that of Neon, or $Ne$. When $N{{a}^{+}}$ion loses an electron, this stable configuration of Neon is broken. This requires a high amount of energy. Hence, the second ionization enthalpy of sodium element is the largest.

So, the correct answer is Option E.

Note: Due to the small size of sodium atom, and higher stability of sodium cation when it loses one electron from its atomic state, the second ionisation enthalpy becomes very high.
Another way to justify it is, when we remove one electron from the sodium atom, the remaining electrons in the atom experience higher effective nuclear charge from the nucleus of the atom, which in turn makes it more difficult to remove the second electron, so it requires much larger energy than before.