State True or False
$C{a^{2 + }}$ has a smaller ionic radius than ${K^ + }$ because it has more nuclear charge.

Hint: Ionic radius of atoms decreases as the number of electrons decreases or loss of electrons leads to decrease in ionic radius because loss of electrons leads to increase in effective nuclear charge.

Complete step by step answer:
We know that the ionic radius of atoms varies by addition or loss of electrons. When an electron is lost by an atom, cation is formed and when electron is gained by an atom anion is formed. Hence an anion acquired a negative charge and cation acquires a positive charge. The ionic radius of cation is smaller than the neutral atom. As in a neutral atom the number of protons and electrons are the same . However when a cation is formed the number of electrons is lesser than the number of protons as a result of the effective nuclear charge ,i.e the tendency of a nucleus to attract the valence electron is increased as a result the ionic radius of cation decreases.
Here we know that the atomic number of $Ca$is 20. Hence the number of electrons in a neutral atom of Ca is 20. When Ca loses two electrons $C{a^{2 + }}$ ion is formed which has 18 electrons.
Also we know potassium(K) has atomic number 19. Hence the number of electrons in the neutral atom of K is also 19. When potassium loses one electron ${K^ + }$is formed which now has 18 electrons. Hence both $C{a^{2 + }}$ and ${K^ + }$ have 18 electrons. The species which has the same number of electrons are known as isoelectronic species.
Now we know as we move left to right in a period atomic number increases ,i.e number of protons increases and the number of shells remains same as a result the effective nuclear charge increases which result in shrinking of size, hence resulting in decrease in ionic radius.
As $C{a^{2 + }}$ and ${K^ + }$ have the same number of electrons but calcium lies after potassium, hence calcium ions have smaller ionic radius than potassium ions.

Hence, the statement that $C{a^{2 + }}$ has smaller ionic radius than ${K^ + }$ because it has more nuclear charge is true.

Note: It should be noted that as we move left to right in a period the ionic radius is decreases due to increase in effective nuclear charge but in groups as we move down in a group due to increase in number of shells the effective nuclear charge is decreases as a result the ionic radius is increases.