Problem 88 - Chemistry An Atoms First Approach

Question

Write the expected electron configurations for each of the following atoms: \(\mathrm{Cl}, \mathrm{Sb}, \mathrm{Sr}, \mathrm{W}, \mathrm{Pb}, \mathrm{Cf}\).

Step-by-Step Solution

Answer

The electron configurations for the given atoms are: Cl (Chlorine): \(1s^2 2s^2 2p^6 3s^2 3p^5\) Sb (Antimony): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^3\) Sr (Strontium): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2\) W (Tungsten): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^4\) Pb (Lead): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^2\) Cf (Californium): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^{10}\)

Step 1: Determine the atomic numbers

Using the periodic table, find the atomic numbers (number of electrons) for each atom. Cl (Chlorine) - Atomic number: 17 Sb (Antimony) - Atomic number: 51 Sr (Strontium) - Atomic number: 38 W (Tungsten) - Atomic number: 74 Pb (Lead) - Atomic number: 82 Cf (Californium) - Atomic number: 98

Step 2: Identify the order of orbitals

We need to know the order in which the orbitals are filled. The order is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

Step 3: Fill in the electrons according to the Aufbau principle, Hund's rule, and Pauli Exclusion Principle

Using the atomic number and order of orbitals, fill in the electrons for each atom: Cl (Chlorine) 1s² 2s² 2p⁶ 3s² 3p⁵ Sb (Antimony) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p³ Sr (Strontium) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² W (Tungsten) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d⁴ Pb (Lead) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p² Cf (Californium) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s² 5f¹⁰

Key Concepts

Aufbau Principle

When it comes to filling the orbitals of atoms with electrons, the Aufbau principle is the navigator. According to this principle, electrons don't just fill into orbitals randomly; they follow a specific 'building up' order, starting from the lowest energy level to higher ones.

Think of it like assigning seats in a theater: the most 'economical' seats (lowest energy orbitals) are taken first. The electrons, much like a hesitant audience, will fill the 1s orbital before moving onto the 2s and so on, progressively moving to seats with a better view (higher energy orbitals) as the lower ones become fully occupied.

Using the Aufbau principle, students can predict the electron configurations for elements by simply following this order, filling each 'seat' with the maximum of two electrons before moving to the next.

Hund's Rule

Imagine a set of roommates (electrons) that have to share a flat (orbital). Hund's rule describes how these electrons will spread out in a subshell. Much like the need for personal space, no electron wants to share its 'room' (orbital) if there are other rooms available.

In technical terms, Hund's rule states that electrons will singly occupy degenerate (equal energy) orbitals before they start to pair up. Electrons are negative and repel each other, so they only pair up when there are no empty rooms left. This distribution also makes the atom more stable, as there's less repulsion between electrons when they're spread out.

For atoms with multiple orbitals of the same energy level, each one should get one electron before any receives a second. An easy way to remember this is 'empty bus seat rule': passengers will usually sit by themselves in an empty row before they sit next to someone else.

Pauli Exclusion Principle

The Pauli Exclusion Principle might sound like a fancy door policy, but it's an essential rule in quantum mechanics related to electrons in an atom. This principle dictates that no two electrons in an atom can have the exact same set of quantum numbers; essentially, each electron must be unique in its properties.

This means that each orbital can hold a maximum of two electrons, and they must have opposite spins. If spins were a social media status, one electron would be 'thumbs up' and the other 'thumbs down.' This ensures that every electron in an atom has a unique state. It's like a strict school dress code, but for electron identity—no twins allowed!

Atomic Numbers

The atomic number is essentially the ID number for elements. It's the number of protons found in the nucleus of an atom, and it dictates the element's identity on the periodic table. But the atomic number isn't just about identity; it also equals the number of electrons in a neutral atom.

This number is crucial when determining an atom's electron configuration, because it tells you exactly how many electrons you need to 'seat' according to the Aufbau principle, Hund's rule, and the Pauli Exclusion Principle. In a way, it's the headcount of electrons that orchestrates the whole arrangement.

Orbital Filling Order

Navigating the orbital filling order is like having a roadmap through the complexities of electron configurations. Here's the gist: not all orbitals are created equal, and they must be filled in a sequence based on their energy levels.

Now, you might think it's as simple as counting 1, 2, 3, and so forth, but quantum mechanical reality offers a unique itinerary. This roadmap starts with '1s', then '2s', and continues on to '2p', '3s', and '3p'. However, after '3p', we take a quantum leap to '4s' before backtracking to '3d'.

Following this order is crucial in writing accurate electron configurations. Akin to steps in a dance routine, missing a step—or an orbital—can lead to a misstep in understanding an atom's electronic structure.