An element $X$ has $12$ protons and $12$ electrons and another element $Y$ has $12$ protons and $10$ electrons. Which element will have larger atomic radii?

Element X has 12 protons and 12 electrons. It is neutral, so the number of protons is equal to the number of electrons. Since the number of protons determines the element's identity, element X is magnesium (Mg), which is in Group 2 of the periodic table.

Element Y has 12 protons and 10 electrons. It has two fewer electrons than magnesium, making it a positively charged ion (cation) with a +2 charge. Since it has lost two electrons from its neutral state, element Y is the magnesium ion (Mg²⁺).

Comparing the atomic radii of these elements:

The atomic radius of element X (neutral magnesium, Mg) is larger than the atomic radius of element Y (magnesium ion, Mg²⁺). This is because, as an ion, element Y has lost two electrons from its neutral state, resulting in a smaller electron cloud and a smaller atomic radius compared to the neutral element X.

Therefore, the correct answer regarding their atomic radii is:

Element X (Mg) has a larger atomic radius than element Y (Mg²⁺).