Arrange the following atoms in order of decreasing atomic radius: \(\mathrm{Na}, \mathrm{Al}, \mathrm{P}, \mathrm{Cl}, \mathrm{Mg} .\)

The periodic table is a fascinating tool that organizes all known elements into a grid of periods (rows) and groups (columns), each with distinctive patterns and trends. One significant trend that is critical for students to comprehend involves the variations in atomic radius, ionization energy, and electronegativity, among others.

As you move from left to right across a period, the atomic radius generally decreases. This occurs because additional protons in the nucleus attract the electron cloud more strongly, pulling it closer to the center. Conversely, as one moves down a group, the atomic radii tend to increase because of the addition of extra electron shells that outweigh the increased nuclear charge.

When discussing atomic radius, one pivotal periodic trend to grasp is the decrease that occurs as one progresses across a period from left to right. To illustrate this, let's consider the elements in the third period.

Every step to the right introduces an additional proton to the nucleus and, usually, an additional electron to the valence shell, the outermost orbital of an atom. This increased positive charge in the nucleus strengthens its pull on the electron cloud, causing the atomic radius to contract. Therefore, it's not just about knowing the trend; it's understanding why it happens—the increased nuclear charge overpowers the shielding effect of inner-shell electrons, drawing the valence shell closer to the nucleus. The solution presented in the textbook step utilizes this principle effectively, explaining why Sodium (Na), being farthest to the left, has the largest atomic radius.

Knowing how to identify an element's group and period is essential to predicting its properties and behavior. The period number of an element corresponds to the highest energy level that its electrons occupy, while the group number can hint at its reactivity and the valence electron count.

For instance, in the given exercise, identifying Sodium (Na) as a Group 1 element alerts you that it has one valence electron and exhibits certain alkali metal traits. Likewise, recognizing that Chlorine (Cl) resides in Group 17 suggests it is a halogen with a tendency to gain an electron.

Combining period and group identification offers a complete picture of the element's electron configuration and allows for accurate predictions of trends like atomic radius. The exercise solution makes use of this by starting the arrangement based on the fact that all elements are within the same period, providing a common ground for comparison.