Problem 13 - Chemistry and Chemical Reactivity

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.

Step-by-Step Solution

Answer

Mg: [Ne] 3s²; Quantum numbers: n=3, l=0, m_l=0, m_s=±1/2 for 3s electrons.

Step 1: Identify Noble Gas Core

Find the noble gas that precedes magnesium in the periodic table. Magnesium (Mg) has an atomic number of 12, and the preceding noble gas is neon (Ne) with an atomic number of 10.

Step 2: Fill Remaining Electrons

Magnesium has 12 electrons. After the neon core, there are 2 electrons left to place. These go into the 3s orbital.

Step 3: Draw Orbital Box Diagram

Represent the electrons with arrows in boxes: - 1s (Ne): \( ext{↑↓}\)- 2s (Ne): \( ext{↑↓}\)- 2p (Ne): \( ext{↑↓}\) \( ext{↑↓}\) \( ext{↑↓}\)- 3s (Mg): \( ext{↑↓}\).

Step 4: Use Noble Gas Notation

Write the configuration starting from the nearest noble gas: \([ ext{Ne}] 3s^2\).

Step 5: Assign Quantum Numbers

For the 3s electrons in magnesium beyond neon, the quantum numbers are: - First electron: - n = 3 (principal quantum number) - l = 0 (s subshell) - m_l = 0 (orbital orientation) - m_s = +1/2 (spin) - Second electron: - n = 3 - l = 0 - m_l = 0 - m_s = -1/2.

Key Concepts

Quantum Numbers

Quantum numbers are like coordinates for electrons, telling us their location and energy. They provide a complete address within an atom by defining specific properties. Each electron has a unique set of four quantum numbers:

• Principal Quantum Number (n): It indicates the main energy level or shell. For example, magnesium's outer electrons are in the 3rd shell, so n = 3.
• Angular Momentum Quantum Number (l): This tells us the shape of the orbital. For s orbitals, like in magnesium, l = 0.
• Magnetic Quantum Number (m_l): It represents the orientation of the orbital in space. For s orbitals, m_l is always 0 because there's only one orientation.
• Spin Quantum Number (m_s): Electrons have a property called spin, which can be either +1/2 or -1/2. In magnesium, one electron in the 3s orbital spins in one direction (+1/2) and the other spins oppositely (-1/2).

Understanding quantum numbers helps us predict an electron's behavior and location within an atom.

Orbital Box Diagram

An orbital box diagram visually shows the distribution of electrons in an atom's orbitals. Each box represents an orbital, and arrows represent electrons. For magnesium, let's break it down:

• 1s, 2s, and 2p Orbitals: These are completely filled by the ten electrons of the preceding noble gas, neon. Each box for these orbitals contains a pair of arrows (↑↓), denoting two electrons with opposite spins.
• 3s Orbital: This orbital is where magnesium’s two outer electrons reside. The diagram would show one box with two arrows (↑↓), indicating that both electrons fill the same orbital with opposite spins.

Orbital diagrams not only help in understanding electron arrangement but also in predicting an atom’s chemical properties.

Noble Gas Notation

Noble gas notation is a shorthand method of writing electron configurations, which makes it convenient and less cluttered. Here's how it works:

• Identify the Noble Gas: Find the noble gas that precedes the element. For magnesium, it is neon (Ne).
• Write the Core Configuration: Use the noble gas symbol in square brackets to represent its complete electron configuration. For magnesium: \([\text{Ne}]\)
• Add Remaining Electrons: Complete the configuration by adding the electrons beyond the noble gas. For magnesium, that's 3s², giving \([\text{Ne}] 3s^2\).

This notation focuses on electrons that are important for chemical reactions, providing a clearer and more concise way to express complex configurations.