On the basis of their positions in the periodic table, select the atom with the larger atomic radius in each of these pairs: (a) \(\mathrm{Na}, \mathrm{Cs} ;\) (b) Be, \(\mathrm{Ba}\); (c) \(\mathrm{N}, \mathrm{Sb}\) (d) \(\mathrm{F}, \mathrm{Br},(\mathrm{e}) \mathrm{Ne}, \mathrm{Xe}\)

Understanding the periodic table is fundamental in chemistry, and one of the most critical aspects is the trend in atomic radius. Let's break this concept down to ensure clarity. As you traverse from left to right across a period in the periodic table, the atomic radius generally decreases. This is due to the increase in the number of protons in the nucleus, which enhances the positive charge and draws the electrons closer. In contrast, as you move down a group, the atomic radius increases. This increase is since each row down adds a new electron shell, moving the outermost electrons further away from the nucleus. It's like climbing a ladder; the higher you go, the further you are from the ground. The increase in the number of electron shells outpaces the pull of the increased positive charge in the nucleus, allowing for an overall larger radius.

For example, in the provided exercise, between Sodium (Na) and Cesium (Cs), Cesium is lower in the group which explains its larger atomic radius. Similarly, Barium (Ba) is below Beryllium (Be) and will have a larger radius. Simple periodic trends like this help students predict and understand the structure and reactions of elements based on their position in the periodic table.

Electron shells are like the layers of an onion surrounding the nucleus of an atom. Each shell can hold a certain number of electrons, with the innermost shell holding up to 2, and successive shells being able to hold more. When the inner shells are filled, electrons start populating the next shell.

In the context of the atomic radius, the more electron shells an atom has, the larger the atom becomes. This concept reflects in the exercise when comparing atoms like Neon (Ne) and Xenon (Xe). Neon is in the second period of the periodic table and has two electron shells while Xenon is in the sixth period, containing more electron shells, thus having a larger radius. It is important to note that the sizes are not proportional to the number of shells due to varying electron-electron repulsions and the increase of protons in the nucleus, but the trend of adding shells leading to a larger radius stands firm.

The vertical columns on the periodic table are called groups, and they reveal a lot about the elements that lie within them. Elements in the same group share similar properties because they have the same number of electrons in their outermost shell, which governs their chemical behavior. This is why elements in the same group often form similar compounds and have similar reactions with other substances.

In terms of atomic radius, all elements within the same group have a trend of increasing radius as you move down the group. This is shown in the earlier exercise comparing elements such as Fluorine (F) and Bromine (Br), both members of Group 17. Bromine, being lower in the group, has a larger atomic radius than Fluorine. Understanding group properties empowers students to predict behaviors and reactions of elements, which is a cornerstone of chemistry.