What causes the trend in atomic radius across a period and within a group?

The atomic radius of an element is a measure of the size of its atoms. The atomic radius of an element can vary depending on its position in the periodic table and on the number of electrons in its outermost energy level (valence electrons).

Across a period, the atomic radius of an element generally decreases as you move from left to right. This trend is due to the increasing number of protons in the nucleus, which attracts the valence electrons more strongly. As a result, the valence electrons are held more closely to the nucleus, causing the atomic radius to decrease.

Within a group, the atomic radius of an element generally increases as you move down the group. This trend is due to the increasing number of energy levels (shells) as you move down the group. As the number of energy levels increases, the valence electrons are farther from the nucleus, causing the atomic radius to increase.

It's worth noting that there are some exceptions to these trends, such as the lanthanides and actinides, which have "abnormal" electron configurations that can cause their atomic radii to behave differently than expected.