Na, Mg, and Al are elements of the 3rd period of the Modern Periodic Table, with group numbers 1, 2, and 13 respectively. Which one of these elements has (a) the highest valency, (b) the largest atomic radius, and (c) the maximum chemical reactivity?

Na, Mg, and Al belong to the third period of the periodic table. Their electronic configurations are:

Na (Z=11): 1s²2s²2p⁶3s¹
Mg (Z=12): 1s²2s²2p⁶3s²
Al (Z=13): 1s²2s²2p⁶3s²3p¹

(a) Highest Valency:
Valency is the combining capacity of an atom. It is determined by the number of electrons in the outermost shell (valence electrons).
Na has 1 valence electron, Mg has 2, and Al has 3. Therefore, Al has the highest valency (3).

(b) Largest Atomic Radius:
Atomic radius decreases across a period from left to right. This is because the effective nuclear charge increases as you move across the period (more protons pulling the electrons closer), while the principal quantum number remains the same. Therefore, Na has the largest atomic radius.

(c) Maximum Chemical Reactivity:
Chemical reactivity is related to the ease with which an atom can lose or gain electrons to achieve a stable electron configuration (usually a full outermost shell, like a noble gas). Alkali metals (Group 1) are highly reactive because they readily lose one electron to attain a noble gas configuration. Alkaline earth metals (Group 2) are less reactive than alkali metals. Group 13 elements are less reactive than Group 2 elements. Therefore, Na has the maximum chemical reactivity among the three elements, due to its lower ionization energy compared to Mg and Al. It is easier for Na to lose one electron than it is for Mg to lose two or Al to lose three.