Question

Write a full set of possible quantum numbers for each of the following: (a) The outermost electron in an \(\mathrm{Li}\) atom (b) The electron gained when a Br atom becomes a Br \(^{-}\) ion (c) The electron lost when a Cs atom ionizes (d) The highest energy electron in the ground-state \(\mathrm{B}\) atom

Short answer

Outermost electron in 1, 0, 0, 1/2: Electron gained by atom becoming import, first , and second

Step-by-step solution

Title - Understanding Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the properties of electrons in orbitals. The four quantum numbers are:1. Principal quantum number ()2. Angular momentum quantum number ()3. Magnetic quantum number ()4. Spin quantum number ()

Title - Outermost Electron in

Determine the quantum numbers for the outermost electron in a atom:1. The electron configuration of is 31.2. The outermost electron is in the orbital.3. Quantum numbers are: 1, 0, 0, and closer to the nucleus.

Title - Electron Gained by Atom Becoming

Determine the quantum numbers for the electron gained by atom to become :1. The electron configuration of is ....2. As the electron is added, it enters the next available orbital.3. Quantum numbers are: import, , , and

Title - Electron Lost by Atom Ionizing

Determine the quantum numbers for the electron lost by atom when it ionizes:1. The electron configuration of is .2. The outermost electron is in the orbital.3. Quantum numbers are: , , and

Title - Highest Energy Electron in

Determine the quantum numbers for the highest energy electron in a atom in the ground state:1. The electron configuration of is .2. The highest energy electron is in the orbital.3. Quantum numbers are , , and

Key concepts

Electron Configuration

Electron configuration refers to how electrons are arranged in an atom's orbitals. It's expressed using notation like \(1s^2 2s^2 2p^6\), which describes where electrons are likely to be found.
Electrons fill orbitals in a specific order based on the energy levels. This order can be remembered using the Aufbau principle, which states that electrons fill the lowest energy orbitals first before moving to higher ones.
For practical purposes, an electron configuration helps determine the chemical properties and reactivity of an element. Understanding how to write and interpret electron configurations can provide insights into electron interactions and the structure of the periodic table.

Principal Quantum Number

The principal quantum number, denoted by \(n\), indicates the main energy level of an electron. It can take positive integer values such as 1, 2, 3, and so on.
This quantum number essentially describes the size and energy of the orbital. The higher the value of \(n\), the farther the electron is from the nucleus and the higher its energy.
For example, in an electron configuration like \(3p^6\), the principal quantum number for the 3p orbital is 3. This tells us that these electrons are in the third energy level.

Angular Momentum Quantum Number

The angular momentum quantum number, denoted by \(l\), describes the shape of the orbital. It can take any integer value from 0 to \(n-1\).
Each value of \(l\) corresponds to a different orbital shape. For example:

• l=0: s-orbital (spherical)
• l=1: p-orbital (dumbbell-shaped)
• l=2: d-orbital (clover-shaped)
• l=3: f-orbital (complex shape)

The angular momentum quantum number helps predict how electrons distribute themselves around the nucleus and influences the atom's chemical properties.

Magnetic Quantum Number

The magnetic quantum number, denoted by \(m_l\), specifies the orientation of the orbital in space. It can take integer values ranging from \(-l\) to \(+l\), including zero.
For instance, if \(l=1\) (a p-orbital), \(m_l\) can be -1, 0, or +1. Each of these values represents a different orientation of the p-orbital.
This quantum number helps further define where an electron is likely to be found relative to the nucleus and allows us to understand the magnetic properties of atoms due to electron positions.

Spin Quantum Number

The spin quantum number, denoted by \(m_s\), describes the intrinsic spin of the electron. It can take one of two values: \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
This quantum number is crucial because it accounts for the electron's magnetic moment and its behavior in a magnetic field. It also plays a fundamental role in the Pauli Exclusion Principle, which states that no two electrons can have the same set of all four quantum numbers.
In summary, the spin quantum number determines the direction of the electron's spin, which can either be up or down.