Question

Draw a partial (valence-level) orbital diagram, and write the condensed ground-state electron configuration for each: (a) Mn (b) \(P\) (c) Fe

Short answer

Mn: [Ar] 4s² 3d⁵, P: [Ne] 3s² 3p³, Fe: [Ar] 4s² 3d⁶.

Step-by-step solution

Write the Atomic Numbers

Determine the atomic numbers of Mn, P, and Fe. Mn has an atomic number of 25, P has an atomic number of 15, and Fe has an atomic number of 26.

Determine the Electron Configuration

Use the atomic numbers to determine the electron configuration for each element. Write out the full electron configuration up to the element:- Mn: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵- P: 1s² 2s² 2p⁶ 3s² 3p³- Fe: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

Write the Condensed Electron Configuration

Convert the full configuration to the condensed form by using the nearest noble gas preceding the element.- Mn: [Ar] 4s² 3d⁵- P: [Ne] 3s² 3p³- Fe: [Ar] 4s² 3d⁶

Draw the Valence-Level Orbital Diagrams

Create the valence-level orbital diagrams:- Mn: 4s: ↑↓ 3d: ↑ ↓ ↑ ↓ ↑- P: 3s: ↑↓ 3p: ↑ ↑ ↑- Fe: 4s: ↑↓ 3d: ↑ ↓ ↑ ↓ ↑ ↑

Key concepts

Atomic Number

The atomic number of an element is the number of protons in its nucleus. It's a unique identifier for each element. For example, manganese (Mn) has an atomic number of 25, phosphorus (P) has an atomic number of 15, and iron (Fe) has an atomic number of 26. These numbers also represent the number of electrons in a neutral atom of each element. So, for a neutral Mn atom, there are 25 electrons, for P there are 15, and for Fe there are 26. Knowing the atomic number is the first step in determining an element's electron configuration. This is crucial because it tells us how many electrons we need to account for when arranging them into orbitals.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. It helps us understand the arrangement of electrons around the nucleus. Electrons occupy energy levels or 'shells', and within those, they fill sublevels (s, p, d, f). The configuration is written as a sequence of these sublevels with superscripts indicating the number of electrons in each. For example, the electron configuration of manganese (Mn) is written as 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵. This shows the filling sequence of electrons starting from the lowest energy sublevel (1s) to the appropriate sublevel for Mn.

Orbital Diagrams

Orbital diagrams are visual representations of how electrons fill subshells and orbitals. Each orbital is represented as a box, and electrons are represented as arrows (↑ and ↓) indicating their spin states. The valence-level orbital diagram focuses on the outermost electrons involved in chemical bonding. When filling orbitals, we follow Hund's Rule, which states that each orbital in a subshell gets one electron before any get two. For example:
- For Mn, the valence-level diagram is 4s: ↑↓ 3d: ↑ ↓ ↑ ↓ ↑.
- For P, it is 3s: ↑↓ 3p: ↑ ↑ ↑.
- For Fe, it is 4s: ↑↓ 3d: ↑ ↓ ↑ ↓ ↑ ↑.
These diagrams help visualize the electron arrangements and predict an element's reactivity and bonding behavior.