No, the size of an atom does not determine its valency. Valency is a term used to describe the combining capacity of an atom to form chemical bonds. It depends on the number of valence electrons an atom has.
Valence electrons are the electrons in the outermost shell of an atom. The valency of an atom is determined by the number of valence electrons it possesses. Elements in the same group of the periodic table (vertical columns) generally have the same number of valence electrons and, therefore, similar valency.
For example, in Group 1 (alkali metals) of the periodic table, elements such as lithium (Li), sodium (Na), and potassium (K) all have one valence electron and exhibit a valency of +1. In Group 17 (halogens), elements like fluorine (F), chlorine (Cl), and bromine (Br) have seven valence electrons and typically exhibit a valency of -1.
While the size of an atom may vary across the periodic table, it does not determine the number of valence electrons or the valency of an atom. Valency is primarily determined by the electron configuration and the number of valence electrons in the outermost shell of an atom.