Question

Using an orbital box diagram and noble gas notation, show the electron configuration of gallium, Ga. Give a set of quantum numbers for the highest- energy electron.

Short answer

[Ar] 4s² 3d¹⁰ 4p¹; Quantum numbers: ( =4, =1, =0, =+1/2)

Step-by-step solution

Determine Atomic Number of Gallium

Gallium (Ga) is an element found on the periodic table with an atomic number of 31. This means that a neutral gallium atom has 31 electrons.

Determine Electron Configuration

The electron configuration is determined by filling the orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The order of filling is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Thus, the electron configuration of gallium is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p¹.

Use Noble Gas Notation

In noble gas notation, electron configurations are abbreviated by starting with the symbol of the nearest noble gas element with fewer electrons. For gallium, the closest noble gas is argon, which has 18 electrons. Therefore, the noble gas notation for gallium is: [Ar] 4s² 3d¹⁰ 4p¹.

Draw the Orbital Box Diagram

The orbital box diagram is a visual representation of the electron configuration. Draw boxes for each orbital, and use arrows to represent electrons: - [Ne] core orbitals filled - 3s : ↑↓ - 3p : ↑↓ ↑↓ ↑↓ - 4s : ↑↓ - 3d : ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ - 4p : ↑ Each box represents an orbital and can hold up to 2 electrons (arrows representing opposite spins). Gallium's highest-energy electrons are in the 4p orbital.

Determine Quantum Numbers for Highest-Energy Electron

The highest-energy electron in gallium is in the 4p orbital. The quantum numbers for this electron are: - Principal quantum number ( ): 4 - Azimuthal quantum number ( ): 1 (p-orbital) - Magnetic quantum number ( ): -1, 0, or +1 (since p-orbitals have three orientations; assume the first is filled) - Spin quantum number ( ): +1/2 or -1/2. Usually, we assume +1/2 for the first electron in an orbital.

Key concepts

Orbital Box Diagram

An orbital box diagram provides a visual way to depict the arrangement of electrons within an atom's orbitals. It's like drawing a map of where electrons "live" within an atom. Each box represents an orbital in which two electrons can reside, depicted by arrows pointing in opposite directions, which show their spins.
The orbital box diagram for gallium would start by filling the lowest energy orbitals first, according to the Aufbau Principle. This principle states that electrons fill orbitals starting from the lowest energy level before moving to higher ones.

• Each occupied orbital is depicted by an arrow.
• Arrows pointing up represent one electron, and down arrows another, indicating opposite spins (following the Pauli Exclusion Principle).
• The filling order follows the 1s, 2s, 2p, 3s, 3p, 4s, 3d, and 4p sequence.

Gallium's orbital box diagram visualizes how all 31 electrons are distributed across its orbitals. For the 4p orbital, you will observe a single upward arrow, as gallium's outermost electron resides there. This diagram effectively shows that the 4p orbital is home to the highest-energy electron in gallium.

Quantum Numbers

Quantum numbers are a set of values used to describe the unique quantum state of an electron within an atom. It's like the unique address for an electron, specifying both its location and properties. Four numbers make up this set:
**Principal Quantum Number (n)**
This number indicates the main energy level occupied by the electron. For gallium's highest-energy electron in the 4p orbital, the principal quantum number is 4.
**Azimuthal Quantum Number (l)**
It defines the shape of the orbital. The number 0 refers to s, 1 to p, 2 to d, and 3 to f orbitals. For a p orbital, like the one gallium's highest-energy electron occupies, l is 1.
**Magnetic Quantum Number (m_l)**
This number specifies the orientation of the orbital in 3D space. For a p orbital, m_l can be -1, 0, or +1. We often choose -1 to begin filling designated orientations.
**Spin Quantum Number (m_s)**
Denoting the electron's spin, this number can be +1/2 or -1/2. It reflects if an electron spins "up" or "down". Typically, for the first electron in a filled orbital, we assume a spin of +1/2. Together, these quantum numbers deliver a complete description of gallium's highest-energy electron positioned within the 4p orbital.

Noble Gas Notation

Noble gas notation is a shorthand for representing electron configurations. Instead of writing out each electron's position from scratch, this method begins with the configuration of the nearest noble gas with fewer electrons, thus saving space and time.
For gallium, located three rows below noble gas argon ([Ar]) on the periodic table, this notation condenses the electron configuration up to that noble gas. Argon, which has 18 electrons, serves as the starting point. From argon's 18 electrons, we simply continue with the remaining sequence, resulting in:

• [Ar] 4s² 3d¹⁰ 4p¹
• The 4s, 3d, and 4p discuss the subsequent electrons gallium hosts beyond those of argon.
• This shorthand communicates that gallium has the same electronic foundation as argon, plus its unique additions.

Noble gas notation not only simplifies electron configurations, making them quicker to write and understand, but also highlights an atom's periodic relationship with the noble gases, aiding in the understanding of chemical behaviors and properties.