Final answer:
Magnesium (Mg) has the smallest atomic radius among aluminum, magnesium, silicon, and sodium, because atomic radii decrease across a period as nuclear charge increases without a corresponding increase in electron shielding.
Step-by-step explanation:
Of the elements aluminum (Al), magnesium (Mg), silicon (Si), and sodium (Na), the one with the smallest atomic radius is Magnesium (Mg). This can be explained by considering the periodic trends. Atomic radii decrease across a period from left to right due to the increase in nuclear charge without a corresponding increase in shielding electrons. Therefore, as we move from sodium to magnesium to aluminum and then to silicon, each element has more protons, pulling the electrons closer and resulting in a smaller atomic radius.
Magnesium is to the left of aluminum and silicon in the periodic table, but is located in a period above both. Therefore, it has fewer electron shells, which makes its atomic radius smaller than that of aluminum and silicon, despite having a larger atomic radius than sodium due to its position further to the right in the same period. Sodium, being in the same period and further to the left, would typically have a larger radius, but it actually has one less electron shell than magnesium, which makes its radius even larger.