The Size of an atom depend on the distance from the nucleus and valence electrons (outermost shell).
As atomic number increases across the period, electrons are added to the same principal shell. So the distance between the valence electrons and nucleus doesn’t change but more protons are added to the nucleus. Therefore, the degree of electrostatic force of attraction between negative and positive charges increases. Electrons are pulled strongly towards nucleus and size decreases.
Down the group, elements have higher atomic number. Valence electrons are added to the last principal shell which are further from the nucleus. So the distance between the nucleus and the valence electrons increases. Overall, atomic radius decreases across the row and increases down the column.
Metallic character: It is defined in terms of tendency to lose electrons. It follows the same trend as atomic size i.e. decreases across the period and increases down t he group. .
Ionization energy: The energy needed to remove the valence electron; usually metals have low Ionization energy, they tend to lose electrons. Nonmetals have high ionization energy. They have tendency to gain electrons. increases across the period and decreases down the group.
The following figure shows atomic size trend and summary of all the periodic trends.