How does atomic radius vary across a period and a group?

Atomic radius decreases across a period from left to right and increases down a group in the periodic table.

In more detail, as you move across a period from left to right, the atomic radius decreases. This is due to the increase in the number of protons in the nucleus as you move across the period. The additional protons increase the positive charge of the nucleus, which pulls the electrons in the outer shell closer to the nucleus, thus decreasing the atomic radius. This effect is greater than the small increase in electron shielding that occurs as you move across a period, so the overall trend is a decrease in atomic radius.

On the other hand, as you move down a group in the periodic table, the atomic radius increases. This is because as you move down a group, a new electron shell is added for each new period. Each new shell is further from the nucleus than the last, which increases the atomic radius. The effect of the additional protons in the nucleus is less significant than the addition of a new electron shell, so the overall trend is an increase in atomic radius.

It's also worth noting that the atomic radius is not a fixed value for a given element, but can vary depending on the element's chemical environment. For example, the atomic radius of an element can be different when it is part of a molecule compared to when it is in its elemental form. However, the trends in atomic radius across periods and down groups are generally consistent regardless of the specific chemical environment.

In summary, the atomic radius is influenced by the number of protons in the nucleus, which affects the positive charge of the nucleus, and the number of electron shells, which affects the distance of the outermost electrons from the nucleus. These factors result in the atomic radius decreasing across a period and increasing down a group in the periodic table.