Question

What is the maximum number of electrons that can occupy each of the following subshells? (a) \(3 s,(\) b) \(2 p,(\mathbf{c}) 4 d\), (d) \(5 s\).

Short answer

The maximum number of electrons that can occupy each subshell are: (a) 3s: 2 electrons, (b) 2p: 6 electrons, (c) 4d: 10 electrons, and (d) 5s: 2 electrons.

Step-by-step solution

Identify the quantum numbers for each subshell

To identify the quantum numbers, we need to know the principal quantum number (n) and the letters corresponding to the orbital angular momentum quantum number (l). Here, s, p, d, and f represent l = 0, 1, 2, and 3, respectively. (a) 3s: n = 3 and l = 0 (b) 2p: n = 2 and l = 1 (c) 4d: n = 4 and l = 2 (d) 5s: n = 5 and l = 0

Calculate the number of electrons for each subshell

Now, use the formula: Number of electrons = 2(2l + 1) to find the maximum number of electrons that can occupy each subshell. (a) 3s: Number of electrons = 2(2(0) + 1) = 2 (b) 2p: Number of electrons = 2(2(1) + 1) = 6 (c) 4d: Number of electrons = 2(2(2) + 1) = 10 (d) 5s: Number of electrons = 2(2(0) + 1) = 2

State the maximum number of electrons for each subshell

(a) The maximum number of electrons that can occupy the 3s subshell is 2. (b) The maximum number of electrons that can occupy the 2p subshell is 6. (c) The maximum number of electrons that can occupy the 4d subshell is 10. (d) The maximum number of electrons that can occupy the 5s subshell is 2.

Key concepts

Quantum Numbers

In the world of atomic structure, quantum numbers play a crucial role. They provide a mathematical description of the unique characteristics of electrons within atoms.

Quantum numbers can be broken down into four different types, each with a specific purpose:

• The Principal Quantum Number (n) determines the energy level and size of the electron cloud.
• The Angular Momentum Quantum Number (l) indicates the shape of the orbital.
• The Magnetic Quantum Number (m_l) gives the orientation of the orbital in space.
• The Spin Quantum Number (m_s) describes the intrinsic spin of the electron.

Without these numbers, determining an electron's location within an atom would be impossible. These numbers guide us in predicting electron configurations and understanding atomic structures in great detail.

The identification of each electron's unique set of quantum numbers serves as a fingerprint for understanding how they behave within an atom.

Subshell Notation

Subshell notation is a shorthand method of expressing the electron configurations in an atom. This notation follows a unique system involving letters and numbers to depict energy levels and orbital types.

Letters such as s, p, d, and f, represent subshells, each corresponding to different angular momentum quantum numbers (l):

• 's' corresponds to l = 0.
• 'p' corresponds to l = 1.
• 'd' corresponds to l = 2.
• 'f' corresponds to l = 3.

The number preceding the letter indicates the principal quantum number (n), i.e., the energy level. This method allows chemists and physicists to easily communicate complex electron configurations.

For instance, using subshell notation for electrons in a 3s shell is simply written as 3s. This kind of notation helps in visualizing the distribution of electrons and makes it easier to understand electron filling order in the periodic table.

Electron Capacity

The electron capacity of a subshell refers to the maximum number of electrons it can hold. This capacity is dictated by the subshell's quantum numbers.

To calculate the electron capacity, one can use the formula:\[\text{Electron Capacity} = 2(2l + 1)\]In this formula, 'l' represents the angular momentum quantum number.

• The 's' orbitals can hold a maximum of 2 electrons (as l = 0).
• The 'p' orbitals can accommodate up to 6 electrons (as l = 1).
• The 'd' orbitals have a capacity of 10 electrons (as l = 2).
• The 'f' orbitals can hold up to 14 electrons (as l = 3).

Understanding electron capacity helps in projecting how elements will behave chemically. It also supports the development of concepts such as chemical bonding, periodic trends, and ionization energy.This fundamental knowledge contributes to advanced studies and applications in chemistry and material sciences.

Principal Quantum Number

The principal quantum number, denoted as 'n', is one of the most basic yet essential quantum numbers. It serves as the primary indicator of the energy level of an electron present in an atom.

The principal quantum number not only provides insight into the electron's energy but also its average distance from the nucleus.

• Electrons with lower n values are closer to the nucleus and have lower energy.
• Higher n values mean the electrons are further away, having higher energy levels.

Furthermore, the principal quantum number determines the size of the electron cloud, which increases with increasing n value. A larger n means a larger orbital and thus a more extensive region in which the electron is likely to be found. The principal quantum number is like a shell encompassing all other quantum properties and is fundamental in defining each electron's status and position within the atom. This concept is pivotal when discussing atom stability, ionization, and chemical properties of elements.