Electrons get added on moving through a group as well as period. Then how can the atomic size decrease in a period but increase in a group?
As you say, atomic size DECREASES across a Period.........
As you say, atomic size DECREASES across a Period, left to right as we face the Table, BUT INCREASES down a Group. Why?
As we add protons to the nucleus, the effective nuclear charge becomes GREATER across the Period. The hydrogen atom is bigger than the helium atom. The helium atom has 2 nuclear charges that attract the 2 electrons in the valence shell drawing them inwards. The lithium atom is bigger than the neon atom. Incomplete electronic shells thus shield the nuclear charge very ineffectively. It is only when the shell becomes full that the nuclear charge is shielded.
And when a shell is full, the next element must start a new Period, and the process begins again, with the valence electrons at an increased radius. This contest between nuclear charge, and shielding by other electrons, underlies the structure of the Periodic Table. And it is a favourite question of examiners.
As a chemist, as a physical scientist, you should look at some data, here is a start. Atomic radii are quoted in
Is the diagram consistent with what I have argued?