From 07909d54dba1d2ea04eb059b317b8a3e8ce1d4f6 Mon Sep 17 00:00:00 2001 From: eggy Date: Mon, 2 Nov 2020 18:54:27 -0500 Subject: [PATCH] chem: complete quantum numbers and add electron configuration --- docs/sch3uz.md | 37 ++++++++++++++++++++++++++++++------- 1 file changed, 30 insertions(+), 7 deletions(-) diff --git a/docs/sch3uz.md b/docs/sch3uz.md index 14d4fc2..53bbfb8 100644 --- a/docs/sch3uz.md +++ b/docs/sch3uz.md @@ -364,7 +364,7 @@ To find the convergence limit **graphically**, graph the difference of frequenci According to **Heisenberg's uncertainty principle**, the more precisely the position of an electron is known, the less precisely its momentum is known and vice versa. Since the Bohr-Rutherford model, like most models, is an egregious lie, this principle is used to develop the Schrödinger model. -The Schrödinger model asserts that electrons are now **three-dimensional waveforms** instead of particles and relates the wave to the electron's energy and position. As such, the position of each electron is represented as a **3D probability cloud** around the nucleus, also known as an **orbital**. +The Schrödinger model asserts that electrons are now **three-dimensional waveforms** instead of particles and relates the wave to the electron's energy and position. As such, the position of each electron is represented as a **3D probability cloud** around the nucleus where the electron is **most likely** to be found, also known as an **orbital**. ### Orbitals @@ -401,7 +401,7 @@ The **Aufbau principle** states that orbitals are filled up in order of increasi (Source: Kognity) -### Electron configuration +### Orbital box diagrams According to **Hund's rule**, atoms fill all orbitals in the same sublevel before pairing up, similar to *Monopoly* house-building rules. @@ -411,7 +411,23 @@ Orbital box diagrams are one method of showing electron configuration by laying These diagrams must show that **energy increases** going up and that there are **spaces** for electrons in labelled orbital **sublevels**. Each electron is represented by an arrow. -By convention, electrons are ordered with the first pointing up and the other pointing down in the same orbital. +By convention, electrons are ordered with the first pointing up and the second pointing down in the same orbital. This is because the **Pauli exclusion principle** states that no two electrons have the same set of quantum numbers, so if one occupies an orbital with a clockwise spin (points up), the other must have an anti-clockwise spin (points down). + +### Electron configuration + +A **full** electron configuration of an element lists each of its orbital sublevels and the number of electrons in each sublevel, ordered in increasing energy. + +(Source: Kognity) + +!!! example + The full electron configuration for bromine ($Z=35$) is: + $$\text{1s}^2\text{ 2s}^2\text{ 2p}^6\text{ 3s}^2\text{ 3p}^6\text{ 4s}^2\text{ 3d}^{10}\text{ 4p}^5$$ + +A **condensed** electron configuration of an element replaces part of the full configuration with the closest noble gas with less electrons enclosed in square brackets. + +!!! example + The condensed electron configuration of bromine is: + $$\text{[Ar] 4s}^2\text{ 3d}^{10}\text{ 4p}^5$$ ### Quantum numbers @@ -419,11 +435,18 @@ Quantum numbers are a set of four numbers that are used to describe the specific The **principal** quantum number ($n$) is the **main energy level** of the electron. -The **angular momentum** quantum number ($l$) is the type of orbital the electron resides in, zero-indexed: +The **angular momentum** quantum number ($ℓ$) is the type of orbital the electron resides in, zero-indexed: - - $l=0$ means that the electron is in an *s*-orbital. - - $l=1$ means that the electron is in a *p*-orbital. - - $l=2$ means that the electron is in a *d*-orbital. + - $ℓ=0$ means that the electron is in an *s*-orbital. + - $ℓ=1$ means that the electron is in a *p*-orbital. + - $ℓ=2$ means that the electron is in a *d*-orbital. + +The **magnetic** quantum number ($m_ℓ$) is contextualised by the angular momentum quantum number and identifies the specific orbital that the electron occupies in its sublevel. The centre orbital is $m_ℓ=0$ and is listed in ascending order. + +!!! example + If $ℓ=1$, $m_ℓ=-2$ indicates that the electron is located in the first *p*-orbital of the sublevel and $m_ℓ=2$ indicates that it is located on the fifth and last *p*-orbital of the sublevel. + +The **spin** quantum number ($m_s$) can either be $\frac{1}{2}$ or $-\frac{1}{2}$ and determines if the electron has a clockwise spin/is the first electron in its orbital or not, respectively. ## 3 - Periodicity