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: Si, \(\mathrm{Al}\), Ge, Ga.

Short answer

The change in atomic radius is smaller when moving left or right within a row because the number of shells remains constant, while moving up or down in a row adds or subtracts an electron shell, causing more significant changes in atomic radius. The order of increasing atomic radius for the elements Si, Al, Ge, and Ga is: Al, Si, Ga, Ge.

Step-by-step solution

(a) Understanding why change in atomic radius is smaller within a row than up or down

Every element in the periodic table consists of protons, neutrons, and electrons. The atomic radius is the distance from the nucleus to the outermost electron orbit, which is mainly affected by the number of protons in the nucleus and the number of occupied electron shells. When moving one place left or right within a row (period) of the periodic table, the number of shells remains constant. Moving left or right will only add or subtract one to the atomic number, meaning there is only one additional or fewer proton and electron that affects the atomic radius. On the other hand, when moving one row up or down (group) in the periodic table, the number of shells increases or decreases by one. A new shell means a significant increase in atomic radius because the distance between the nucleus and the outermost electrons will increase. In summary, the change in atomic radius is smaller when moving left or right within a row because the number of shells remains constant, while moving up or down in a row adds or subtracts an electron shell, causing more significant changes in atomic radius.

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

In order to arrange the elements in order of increasing atomic radius, we can refer to the positions of these elements in the periodic table. Here are the positions of the given elements: - Silicon (Si) is in Group 14 (IV) and Period 3 - Aluminum (Al) is in Group 13 (III) and Period 3 - Germanium (Ge) is in Group 14 (IV) and Period 4 - Gallium (Ga) is in Group 13 (III) and Period 4 As we know from part (a) of this exercise, the changes in atomic radius are more significant when moving up or down compared to moving left or right. So, elements in Period 3 will generally have smaller atomic radii compared to those in Period 4. Now, we can arrange the elements in order of increasing atomic radius based on their positions in the periodic table: 1. Aluminum (Al) - since it is in Period 3 and to the left of Si 2. Silicon (Si) - since it is in Period 3 3. Gallium (Ga) - since it is in Period 4 and to the left of Ge 4. Germanium (Ge) - since it is in Period 4 So, the order of increasing atomic radius is: Al, Si, Ga, Ge.

Key concepts

periodic table

The periodic table is a fascinating and valuable tool for understanding the elements. It organizes elements in order of increasing atomic number, which represents the number of protons found in an atom's nucleus.
The layout of the periodic table allows us to observe patterns and trends among the elements.
This arrangement brings out periodic trends, such as variations in atomic radius, which is the size of an atom.

• Rows, known as periods, indicate elements with the same number of electron shells.
• Columns, or groups, show elements with similar chemical properties due to having the same number of valence electrons.

Understanding the structure of the periodic table can help us predict element properties, including atomic radius, without needing to look up each element's individual data.

electron shells

Electron shells are essentially layers of electrons surrounding the nucleus of an atom. Each shell can hold a certain number of electrons and fills up in a specific order.
The more shells an atom has, the larger its atomic radius will be because the outermost electrons are further from the nucleus.
The arrangement of electron shells follows a pattern determined by quantum mechanics.

• The first shell can hold up to 2 electrons.
• The second shell can hold up to 8 electrons.
• Subsequent shells can hold more electrons, with rules dictated by more complex quantum numbers.

In the periodic table, each row or period represents a completed set of these shells, providing a visual guide to understanding how atomic size increases with additional shells.

atomic number

The atomic number is a defining characteristic of an element. It represents the number of protons in an atom's nucleus and is crucial in determining the element's identity.
The atomic number not only tells us the count of protons but also the number of electrons in a neutral atom, as electrons balance the positive charge of the protons.
As you move across a period in the periodic table, elements increase by one atomic number at a time. This increase impacts the atomic radius slightly:

• Adding electrons increases electrostatic attraction to the nucleus, potentially reducing the atomic radius slightly.
• The increase varies less within a period since the number of electron shells remains constant.

The atomic number is key in identifying how elements will react, as well as understanding why changes in atomic size are less pronounced across periods than down groups.

nonmetallic elements

Nonmetallic elements are found primarily on the right side of the periodic table. These elements are known for their lack of metallic properties and diverse range of physical forms and chemical behaviors.
Nonmetals typically have higher electronegativities and ionization energies compared to metals, which makes them more likely to gain electrons rather than lose them.
In terms of atomic radius:

• Nonmetals generally have smaller atomic radii compared to metals within the same period because added protons lead to a stronger pull on electrons, reducing the radius.
• Their atomic radii decrease moving from left to right across a period similar to metals but increase significantly moving down a group due to additional electron shells.

Understanding nonmetals is key to mastering chemical reactions and molecule formation, as they play crucial roles in a vast array of compounds and materials.