why does atomic size decrease cross a period? why does atomic size increase down a group?

As one moves from left to right on the periodic table, the nucleus is increasing its positive charge so the pull on the outside electrons is greater and that decreases the size somewhat. As one moves down the periodic table, the electrons are being added to another shell and that makes the size larger.

The atomic size is influenced by two main factors: the number of energy levels (or shells) occupied by electrons and the effective nuclear charge. Let's break down how these factors explain the trend of atomic size across a period and down a group.

1. Atomic size across a period (left to right):
As we move from left to right across a period, the atomic size generally decreases. This is due to the increasing number of protons in the nucleus, which leads to a greater effective nuclear charge—the attractive force between the positively charged nucleus and negatively charged electrons. The stronger attractive force pulls the electrons closer to the nucleus, resulting in a smaller atomic size.

Additionally, the number of energy levels or electron shells remains the same across a period. The increase in the positive charge of the nucleus is not effectively shielded by the inner electrons, resulting in a stronger nuclear pull on the outermost electrons.

2. Atomic size down a group (top to bottom):
When we move down a group in the periodic table, the atomic size generally increases. This is primarily because each subsequent element has an additional energy level (shell) occupied by its electrons. As more energy levels are added, the electrons are farther away from the nucleus, resulting in a larger atomic size.

Furthermore, the effective nuclear charge is relatively constant within a group. The increase in the number of protons is accompanied by a proportional increase in the number of inner electrons, which shield the outer electrons from the attractive force of the nucleus. Therefore, the increase in atomic size is mainly attributed to the addition of energy levels.

In summary, the decreasing atomic size across a period is due to the increasing effective nuclear charge outweighing the constant number of energy levels. On the other hand, the increasing atomic size down a group is primarily a result of the addition of energy levels while keeping the effective nuclear charge relatively constant.