How do the sizes of atoms change as we move (a) from left to right across a row in the periodic table, (b) from top to bottom in a group in the periodic table? (c) Arrange the following atoms in order of increasing atomic radius: \(\mathrm{O}, \mathrm{Si}, \mathrm{I}, \mathrm{Ge} .\)

Atomic size or atomic radius is a measure of the size of an atom. It is the distance between the nucleus and the outermost electron shell. Atomic size is generally measured in picometers (pm).

As we move across a period in the periodic table, the number of protons in the nucleus increases, which leads to an increase in the effective nuclear charge. The effective nuclear charge (Z_eff) is the net positive charge experienced by the electrons in the outermost electron shell. A higher effective nuclear charge results in more tightly held electrons, which causes the electron cloud to contract and the atomic size to decrease.

As we move from left to right across a row (period) in the periodic table, the atomic number increases, leading to an increase in the number of protons and electrons. This causes the effective nuclear charge to increase, making the outer electrons feel a stronger attraction to the nucleus. As a result, the atomic size decreases from left to right across a period.

When we move down a group in the periodic table, the atomic number increases, which leads to an increase in the number of electron shells. The outermost electron shell is now further away from the nucleus, and the additional electron shells shield the outer electrons from the effective nuclear charge. This results in a weaker attraction between the nucleus and the outer electrons, hence the atomic size increases from top to bottom in a group.

We need to arrange O (Oxygen), Si (Silicon), I (Iodine), and Ge (Germanium) in order of increasing atomic radius. Looking at the periodic table, we can see that Oxygen (O) is in period 2 and group 16, Silicon (Si) is in period 3 and group 14, Iodine (I) is in period 5 and group 17, and Germanium (Ge) is in period 4 and group 14. Using our understanding of how atomic sizes change in the periodic table: 1. O and Si: Moving from O to Si is moving down a group, and therefore the atomic size increases. So, Si has a larger atomic radius than O. 2. Si and Ge: Moving from Si to Ge is moving down a group, and therefore the atomic size increases. So, Ge has a larger atomic radius than Si. 3. Ge and I: Moving from Ge to I is moving down a group but also moving one element to the right (across the period), as a result, the atomic radius of I will be slightly larger than Ge. Based on this, we can arrange O, Si, I, Ge in order of increasing atomic radius: O < Si < Ge < I.