Question

What is wrong with the following electron configurations for atoms in their ground states? (a) \(\mathrm{ls}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{1}\) (b) \([\mathrm{Ne}] 2 s^{2} 2 p^{3}\) (c) \([\mathrm{Ne}] 3 s^{2} 3 d^{5}\)

Short answer

The electron configurations have the following issues: (a) The given configuration misses the \(2p\) orbital. The correct configuration is \(\mathrm{1s}^{2} 2 \mathrm{s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{s}^{1}\). (b) The given configuration incorrectly goes back to \(2s\) and \(2p\) orbitals after the \([\mathrm{Ne}]\) notation. The correct configuration is \([\mathrm{Ne}] 3 \mathrm{s}^{2} 3 \mathrm{p}^{1}\). (c) The given configuration skips the \(3p\) orbitals. The correct configuration should be \([\mathrm{Ne}] 3 \mathrm{s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{s}^{2} 3 \mathrm{d}^{5}\).

Step-by-step solution

(a) \(\mathrm{1s}^{2} 2 \mathrm{s}^{2} 3 \mathrm{s}^{1}\)#

The given electron configuration is missing an important component: the \(\mathrm{p}\) orbital. After the filled \(\mathrm{2s}\) orbital, there should be a \(\mathrm{2p}\) orbital before moving on to the \(\mathrm{3s}\) orbital. The corrected electron configuration should look like this: \(\mathrm{1s}^{2} 2 \mathrm{s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{s}^{1}\).

(b) \([\mathrm{Ne}] 2 \mathrm{s}^{2} 2 \mathrm{p}^{3}\)#

The given electron configuration starts with the \([\mathrm{Ne}]\) notation, which means that we start with the electron configuration of neon (\(\mathrm{1s}^{2} 2 \mathrm{s}^{2} 2 \mathrm{p}^{6}\)). However, after this starting point, the electron configuration violates the Aufbau Principle by going back to the \(\mathrm{2s}\) and \(\mathrm{2p}\) orbitals. The corrected electron configuration should be \([\mathrm{Ne}] 3 \mathrm{s}^{2} 3 \mathrm{p}^{1}\).

(c) \([\mathrm{Ne}] 3 \mathrm{s}^{2} 3 \mathrm{d}^{5}\)#

The given electron configuration starts with the \([\mathrm{Ne}]\) notation, so we again start with the electron configuration of neon (\(\mathrm{1s}^{2} 2 \mathrm{s}^{2} 2 \mathrm{p}^{6}\)). After this starting point, it follows the \(\mathrm{3s}\) and \(\mathrm{3d}\) orbitals correctly. However, it completely skips the \(\mathrm{3p}\) orbitals, which violates the Aufbau Principle. The corrected electron configuration should be \([\mathrm{Ne}] 3 \mathrm{s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{s}^{2} 3 \mathrm{d}^{5}\).

Key concepts

Aufbau Principle

When we talk about the Aufbau Principle, we're looking at a fundamental guideline for figuring out how electrons occupy orbitals within an atom. Think of it as a map that electrons follow when they 'settle' into an atom. The principle's name comes from the German word 'Aufbau,' meaning 'building up,' and it describes exactly that: how to build up the electron configuration of an element, one electron at a time.

The rule is fairly simple – electrons fill orbitals starting with the lowest energy level and move to higher levels progressively. But remember, orbitals within the same energy level don't always have the same energy. That's why the 1s orbital is filled before the 2s, and the 2s is filled before the 2p. This sequence continues in a specific order known as the 'electron configuration order.'

Here's an important thing to keep in mind: each orbital can hold up to two electrons. And if you have multiple orbitals at the same energy level – like the three p orbitals in the 2p subshell – you need to add one electron to each before you start pairing them up. This is known as Hund's Rule, and it goes hand-in-hand with the Aufbau Principle.

Orbital Notation

Now, let's unpack this concept of 'orbital notation,' which is like a visual shorthand for electron configurations. It helps you keep track of which orbitals are filled and which ones are still waiting for electrons. In an orbital notation diagram, each orbital is represented by a box (or a line), and electrons are indicated by arrows. An up arrow \( \uparrow \) means one electron with a certain spin, and a down arrow \( \downarrow \) represents another electron with the opposite spin in the same orbital.

Why use arrows, you ask?

Well, it's because of a quantum mechanical property called 'spin.' Each electron has this tiny inherent angular momentum, and pairing them with opposite spins keeps them energetically stable inside an orbital. So, for a complete visual, imagine a set of boxes with arrows in them. This visualization makes it a lot easier to see where the electrons are and how the orbitals fill up according to both the Aufbau Principle and Hund's Rule.

Orbital notation is not just for show – it's an effective tool to avoid mistakes like the ones encountered in the earlier exercise. It lets you see at a glance if you've accidentally skipped an orbital or put too many electrons in one place.

Quantum Mechanics in Chemistry

Quantum mechanics is not just theoretical; it's the science behind the behaviors of electrons in chemistry and, by extension, has a huge impact on how we understand chemical reactions and properties of materials. In the quantum world, we step away from the orbits of Bohr's model and move towards orbitals – regions in space where there's a high probability of finding an electron.

What makes quantum mechanics fascinating is its ability to explain the 'why' and 'how' of electron arrangement. Electrons in atoms exist in discrete quantum states, defined by four quantum numbers that tell us their energy, shape, orientation, and spin. These numbers aren't just random; they're rooted in the Schrödinger equation, a cornerstone of quantum mechanics that allows us to determine the probability of finding an electron in a particular space.

The quantum approach is crucial because it gives rise to the principles and rules discussed earlier – the Aufbau Principle, Hund's Rule, and Pauli Exclusion Principle (which states that no two electrons in an atom can have the same set of four quantum numbers). So, when you're using orbital notation or adhering to the Aufbau Principle, you're actually applying quantum mechanics to make sense of the micro-world of atoms.