Question

Depict the electron configuration for magnesium using an orbital box diagram and noble gas notation. Give a complete set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.

Short answer

[Ne] 3s²; The 3s electrons have quantum numbers: (3, 0, 0, +1/2) and (3, 0, 0, -1/2).

Step-by-step solution

Identify the Atomic Number

Magnesium has an atomic number of 12, meaning it has 12 electrons in its neutral state.

Write the Full Electron Configuration

The electron configuration for magnesium (Mg) is written as: \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \]This shows that all 12 electrons are accounted for across these orbitals.

Determine Noble Gas Notation

Identify the preceding noble gas to simplify the configuration. The noble gas before magnesium is neon, with the electron configuration \[ [Ne] = 1s^2 \, 2s^2 \, 2p^6 \]Therefore, the noble gas shorthand for magnesium is: \[ [Ne] \, 3s^2 \]

Draw the Orbital Box Diagram

The box diagram for magnesium up to 3s is represented as:\[\begin{array}{c|c|c|c}1s & \uparrow\downarrow & & \2s & \uparrow\downarrow & & \2p & \uparrow\downarrow & \uparrow\downarrow & \uparrow\downarrow \3s & \uparrow\downarrow & & \\end{array}\]Each box represents an orbital, and arrows indicate the electrons with opposing spins.

Examine Quantum Numbers for 3s Electrons

For the two electrons in the 3s orbital (the electrons beyond neon), the quantum numbers are: - First electron in 3s: - Principal Quantum Number (n) = 3 - Angular Momentum Quantum Number (l) = 0 (s orbital) - Magnetic Quantum Number (m_l) = 0 (since it's only one possible orientation for s) - Spin Quantum Number (m_s) = +1/2 - Second electron in 3s: - Principal Quantum Number (n) = 3 - Angular Momentum Quantum Number (l) = 0 - Magnetic Quantum Number (m_l) = 0 - Spin Quantum Number (m_s) = -1/2

Key concepts

Orbital Box Diagram

The orbital box diagram is a visual tool used in chemistry to represent the distribution of electrons across different orbitals in an atom. Think of it like packing items into boxes — each orbital gets its own box, and electrons are the items being placed inside. For magnesium, we want to distribute 12 electrons.

In an orbital box diagram, orbitals are represented as boxes, and electrons are represented as arrows pointing either up or down. These arrows indicate an electron's spin. Keep in mind:

• Each orbital can hold two electrons.
• Electrons in the same orbital have opposite spins, shown as arrows pointing in opposite directions.
• Fill lower energy orbitals first, following the Aufbau principle.

For magnesium's electron configuration \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \], we would draw separate boxes for 1s, 2s, 2p, and 3s. The 1s orbital gets its first two electrons, represented as one up arrow and one down arrow in the 1s box.

Continue this for 2s and 2p, and finally, place two arrows for 3s. This completes magnesium's electron configuration with a balanced and visually clear distribution of electrons across the orbital boxes.

Quantum Numbers

Quantum numbers are the address system for electrons within an atom, defining their position and characteristics within atomic orbitals. For the electrons in magnesium's 3s level, these quantum numbers are crucial for understanding their configuration.

There are four quantum numbers:

• Principal Quantum Number (n): This defines the energy level. For the 3s electrons of magnesium, we set \( n = 3 \).
• Angular Momentum Quantum Number (l): This determines the shape of the orbital. The value for an s orbital is \( l = 0 \).
• Magnetic Quantum Number (m_l): This specifies the orientation of the orbital in space. For an s orbital, this number is always \( m_l = 0 \) due to its spherical shape.
• Spin Quantum Number (m_s): This describes the electron’s spin direction, which can be \( +1/2 \) or \( -1/2 \). These are shown as up or down arrows in the orbital box diagram.

For the 3s electrons in magnesium, each electron will have:

• First electron: \( n = 3, l = 0, m_l = 0, m_s = +1/2 \)
• Second electron: \( n = 3, l = 0, m_l = 0, m_s = -1/2 \)

These properties pinpoint the exact identity and behavior of these electrons in their respective orbitals.

Noble Gas Notation

Noble gas notation is a shorthand method to express the electron configuration of an element. It simplifies the writing process by focusing just on the electrons added beyond the last noble gas.

The beauty of using noble gas notation comes from reducing complex electron configurations into manageable parts. For magnesium, the noble gas preceding it is neon, denoted as \([Ne]\), which covers the electron configuration \( 1s^2 \, 2s^2 \, 2p^6 \).

• This allows us to write the electron configuration for magnesium as \([Ne] \, 3s^2\).
• It shows only the arrangement of electrons added after neon, using a compact and efficient expression.

Using noble gas notation not only saves time in writing but also highlights the valence electrons directly, which are often the electrons involved in chemical reactions.

This method is widely accepted and appreciated in both academic and practical chemistry contexts, allowing students and professionals alike to focus on key differences among elements without rewriting their entire configurations.