Question

Draw orbital diagrams for atoms with the following electron configurations: (a) \(1 s^{2} 2 s^{2} 2 p^{5}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{7}\)

Short answer

(a) 2p has one paired electron. (b) 3p has three unpaired electrons. (c) 3d has two paired and three unpaired electrons.

Step-by-step solution

Understanding Electron Configuration

Before drawing the orbital diagrams, recall that each subshell (s, p, d, f) has a specific number of orbitals and each orbital can hold a maximum of 2 electrons. The s subshell has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7 orbitals.

Orbital Diagram for (a)

For the electron configuration \(1s^2 \ 2s^2 \ 2p^5\), the orbital diagram is:1. **1s Orbital:** Two up and down arrows to indicate 1 pair (filled orbital).2. **2s Orbital:** Two up and down arrows to indicate 1 pair (filled orbital).3. **2p Orbitals:** Three boxes (orbitals), fill first with one arrow each (representing electrons in separate orbitals with parallel spins) then place a second electron in one of the orbitals: | ↑ | ↑ | ↑ | | ↓ | | |

Orbital Diagram for (b)

For the electron configuration \(1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^3\), the orbital diagram is:1. **1s Orbital:** Two up-down arrows (filled orbital).2. **2s Orbital:** Two up-down arrows (filled orbital).3. **2p Orbitals:** Six electrons fill the three orbitals completely. Each box has arrows both up and down: | ↑↓ | ↑↓ | ↑↓ |4. **3s Orbital:** Two up-down arrows (filled orbital).5. **3p Orbitals:** Three boxes. Like 2p in Step 2, fill with one arrow in each: | ↑ | ↑ | ↑ |

Orbital Diagram for (c)

For the electron configuration \(1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^7\), the orbital diagram is:1. **1s, 2s, and 3s Orbitals:** Each filled with two arrows (each a filled orbital combination of up and down arrows).2. **2p and 3p Orbitals:** Fully filled similar to previous examples: | ↑↓ | ↑↓ | ↑↓ | (both for 2p and 3p)3. **4s Orbital:** Two up and down arrows (filled orbital).4. **3d Orbitals:** Five boxes, seven electrons are distributed as follows: - Fill the first five boxes with one upwards arrow each (Hund's Rule for maximum unpaired electrons). - Next, pair electrons in two orbitals: | ↑↓ | ↑↓ | ↑ | ↑ | ↑ |

Completed Orbital Diagrams

We have now completed the orbital diagrams for each electron configuration. - (a) reflects a Fluorine atom. - (b) reflects a Phosphorus atom. - (c) reflects a Cobalt atom.

Key concepts

Electron Configuration

Electron configuration is a method used to describe the arrangement of electrons in an atom. It's an essential concept for understanding how atoms interact and bond with each other. By following the sequence of energy levels and subshells (s, p, d, f), we can predict and illustrate the distribution of electrons within an atom.
Electrons fill the available subshells starting from the lowest energy level to the highest. The order follows the Aufbau principle. The sequence generally starts with the 1s subshell, progressing through 2s, 2p, 3s, 3p, 4s, and so on. This method highlights how electrons populate atomic orbitals and provides insight into an atom's reactivity. Understanding electron configuration helps us delve into the chemistry behind periodic table trends and the resulting chemical properties of elements.

Hund's Rule

Hund's Rule provides guidance when filling orbitals with electron pairs. This rule states that electrons will fill an unoccupied orbital before pairing with an electron in an already occupied one. This ensures the most stable arrangement possible by maximizing unpaired electrons within a subshell.
According to Hund's Rule, within a p, d, or f subshell, electrons will first occupy separate orbitals with parallel spins, resembling the filling of seats on a bus: individuals choose empty rows before pairing up. This arrangement minimizes electron-electron repulsions, thus stabilizing the atom. Hund's Rule helps predict the electron placement within subshells and influences magnetic properties and chemical reactivity.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental principle in quantum mechanics. It states that no two electrons within an atom can have the same set of four quantum numbers. This translates to a maximum of two electrons per orbital, and these must have opposite spins: typically represented as an up and a down arrow.
This principle is crucial for electron configuration as it maintains the unique identity of each electron within an atom. Without it, the diversity of chemical properties that arise from different electron configurations couldn't exist. The Pauli Exclusion Principle essentially governs how electrons fill available orbitals, contributing to the exclusivity of the electronic arrangement for each element.

Subshells in Chemistry

Subshells in chemistry refer to divisions within electron shells where electrons reside. Each shell can contain one or more subshells, and these are named s, p, d, and f. Understanding subshells helps in comprehending how electrons are organized in atoms, which is pivotal for predicting chemical behavior.
- **s Subshell:** Contains 1 orbital and can hold up to 2 electrons.
- **p Subshell:** Contains 3 orbitals and can hold up to 6 electrons.
- **d Subshell:** Contains 5 orbitals with a capacity of 10 electrons.
- **f Subshell:** Contains 7 orbitals and can accommodate 14 electrons.
Every element’s electrons are arranged following this structure, filling from lower to higher energy subshells. Comprehending subshell arrangement is vital for tasks like predicting an element's place on the periodic table or its chemical reactivity.