Question

(a) Among the nonmetallic elements, the change in atomic radius in moving one place left or right in a row is smaller than the change in moving one row up or down. Explain these observations. (b) Arrange the following atoms in order of increasing atomic radius: \(S i\). \(\mathrm{A} 1\), Ge, Ga.

Short answer

The atomic radius generally increases as we move across a period (left to right) and decreases as we move down a group (top to bottom) in the periodic table. In non-metallic elements, the change in atomic radius across a period is less significant due to strong electron-electron repulsion. The atomic radius trends can be explained by considering effective nuclear charge (Z_eff) and the number of electron shells. For the given elements, the increasing order of atomic radius is Al < Si < Ga < Ge.

Step-by-step solution

(a) Explain the observation regarding the change in atomic radius in periodic table rows and columns

The atomic radius is the measure of the size of an atom. In the periodic table, elements are arranged in rows and columns according to their atomic number. This arrangement reflects how electrons fill the atomic orbitals and reveal the periodic trends in their properties, including atomic radii. In general, the atomic radius increases as we move across a period (left to right) and decreases as we move down a group (top to bottom). There are two main factors that influence these trends: the effective nuclear charge (Z_eff) experienced by the electrons and the number of electron shells. As we move left to right in a row, the atomic number increases, meaning there are more protons in the nucleus and electrons in the electron cloud. However, the electrons are added to the same energy level, so the shielding effect of the inner electrons remains relatively constant. Therefore, the Z_eff increases, and the outer electrons are pulled closer to the nucleus, resulting in a smaller atomic radius. However, the change in atomic radii is less significant in non-metallic elements, possibly due to strong electron-electron repulsion as atomic radius decreases further. When moving down a group, the atomic number also increases, but in this case, electrons are added to a new energy level that is further from the nucleus. This new electron shell creates more shielding, and the Z_eff increases at a slower rate than in a row. As a result, the outer electrons are not pulled significantly closer to the nucleus, and the atomic radius increases.

(b) Arrange Si, Al, Ge, Ga in order of increasing atomic radius

To arrange these elements in order of increasing atomic radius, we need to consider their positions in the periodic table and apply the trends discussed in part (a). 1. Silicon (Si) is in period 3 and group 14. 2. Aluminum (Al) is in period 3 and group 13. 3. Germanium (Ge) is in period 4 and group 14. 4. Gallium (Ga) is in period 4 and group 13. Based on the trends explained earlier, we expect the atomic radii to increase as we move down a group and increase as we move left in a row. So, we can arrange the elements in order of increasing atomic radius as follows: Al < Si < Ga < Ge Al and Si are in the same period (3), and Al is to the left of Si, so Al has a larger atomic radius than Si. Ge and Ga are in the same period (4), and Ga is to the left of Ge, so Ga has a larger atomic radius than Ge. Since both Ga and Ge are in period 4, which is below period 3, they tend to have larger atomic radii than Al and Si.

Key concepts

Periodic Table

The periodic table is a wonderful tool for understanding the properties of elements, including their atomic radius. It organizes elements horizontally into periods and vertically into groups based on their atomic numbers. Each element's atomic number tells us how many protons are in its nucleus, which in turn influences its electron configuration and chemical behavior.
As we move across a period from left to right, electrons are added one by one into the same energy level. This results in a gradual decrease in atomic radius since the electrons feel a stronger pull toward the nucleus. In contrast, moving down a group adds electrons to new, additional energy levels or shells, increasing the atomic size. This layout of the periodic table allows us to identify and predict trends, like atomic size, with remarkable accuracy.

Effective Nuclear Charge

Effective Nuclear Charge, often denoted as \( Z_{eff} \), is a key factor in understanding why atomic size changes as you move across or down the periodic table. It is the net positive charge experienced by the valence electrons in an atom.

• Across a period, the number of protons increases, leading to a higher nuclear charge.
• The electrons are added to the same outer shell, so their repulsion doesn't significantly offset the increasing pull from the nucleus.

Thus, the \( Z_{eff} \) experienced by electrons increases as more protons are packed into the nucleus, pulling outer layer electrons inwards and decreasing the atomic radius.
However, within a group, although the nuclear charge increases, new energy levels are also added. The increased distance and additional electron-electron repulsion in these new energy shells gradually outweigh the nuclear charge, resulting in larger atoms.

Electron Shells

Electron shells are layers around an atom's nucleus where electrons reside. Imagine them as rings that have increasing distances from the nucleus. As you go further from the nucleus, the shells can hold more electrons. Their presence and number are crucial to determining an atom's size.
When a new shell is added, which happens as you go down a group in the periodic table, the atomic radius increases. This is because each new shell makes the outer electrons further away from the nucleus, leading to a bigger atomic size.

• Higher energy levels = further distance from nucleus = larger atomic radius.
• More inner shells lead to greater shielding of outer electrons from the nucleus’ pull, allowing them to spread out more easily.

Understanding electron shells helps explain why atomic radii increase drastically with each row down the table.

Periodic Trends

Periodic trends are patterns within the periodic table that show how particular properties of elements change across and down the table. These trends are essential for predicting and explaining the behavior of elements.
The atomic radius trend is one of the most fundamental. Across a period, atoms become smaller because more protons mean a stronger pull on the electrons, compacting them closer to the nucleus. Down a group, atoms grow larger because of the addition of new shells.

• Across a period (left to right): Atomic radius decreases due to increasing \( Z_{eff} \).
• Down a group (top to bottom): Atomic radius increases as new electron shells are added.

Other trends include electronegativity, ionization energy, and metallic character, all affected by the same principles of nuclear charge and electron shielding. Understanding these trends offers valuable insights into chemical reactivity and element characteristics.