Question

why does the atomic size decreases across the period and increases down the period in the modern periodic table​

Answer 1

Additionally, as the atomic number increases, the effective nuclear charge also increases. ... Therefore, moving left to right across a period the nucleus has a greater pull on the outer electrons and the atomic radii decreases. Moving down a group in the periodic table, the number of filled electron shells increases.

Answer 2

The atomic size of an element

In a Period : On moving from left to right in a period , the size of the atom decreases.

As we move from left to right in a period, the atomic number of an element increases which means that the number of protons and electrons int the atom increases ( the extra electrons is added to the same shell) .Due to the large positive charge on the nucleus , the electrons are pulled in more closer to the nucleus and the size of the atom decreases.

In a Group : On moving from top to bottom the size of the atom increases.

This is because the number of shells are increasing as we go down the group.

Hope this helps...