Chemistry (9701) | Electrons, energy levels and atomic orbitals

Chemistry 9701: Electrons, Energy Levels, and Atomic Orbitals (1.3)

Welcome to one of the most fundamental and important topics in Chemistry! Understanding how electrons are arranged in an atom is the key to explaining almost everything else we study—from bonding to reactivity and the patterns in the Periodic Table.

Don't worry if terms like 'orbital' sound complicated. We are going to break down the atom's electron structure using simple analogies, turning it from a mystery into a logical system!

1. The Electron Address System: Shells, Sub-shells, and Orbitals

Imagine the atom as a city, and the nucleus is the City Hall. The electrons don't just fly randomly; they live in specific zones. We describe their location using three key terms: shells, sub-shells, and orbitals.

Key Definitions (LO 1.3.1)

• Principal Quantum Number (\(n\)): This is the main energy level, or the "floor" in our electron hotel analogy. The higher the value of \(n\) (1, 2, 3, 4, etc.), the further the electron is from the nucleus and the higher its energy.
• Shells: These are the major energy levels identified by \(n\). The shells fill sequentially starting from \(n=1\) (the inner shell).
• Sub-shells: These are "types of rooms" found within a shell. They are labeled s, p, d, and f.
  • \(n=1\) has only 1 sub-shell: s
  • \(n=2\) has 2 sub-shells: s and p
  • \(n=3\) has 3 sub-shells: s, p, and d
  • \(n=4\) has 4 sub-shells: s, p, d, and f (though we only focus on 4s and 4p for AS Level).
• Atomic Orbitals: These are specific regions of space within the sub-shell where there is the highest probability (about 95%) of finding an electron. Think of these as the individual bedrooms.
• Ground State: This is the most stable state of an atom where the electrons occupy the lowest possible energy levels available. This is the configuration we always aim to determine.

2. The Shapes of Orbitals (LO 1.3.8)

The shape of an orbital describes the region of space where the electron spends its time.

• s orbitals:

  These are spherical in shape. They are non-directional, meaning the electron density is the same in all directions from the nucleus. The 1s, 2s, and 3s orbitals are all spherical, but they increase in size as \(n\) increases.

• p orbitals:

  These are dumbbell (or peanut) shaped. They are directional. Since the p sub-shell contains 3 orbitals, these three orbitals are oriented along the three axes in space: the x-axis, the y-axis, and the z-axis. We label them \(p_x\), \(p_y\), and \(p_z\).

3. The Order of Filling: Energy Levels (LO 1.3.3)

Electrons fill orbitals starting from the lowest energy level (the ground state). If you are building an atom, you follow the principle of lowest energy first.

The Energy Ladder

The observed order of increasing energy for the sub-shells we need to know is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

4. How to Write Electronic Configurations

To determine the electronic configuration, we follow three main rules which ensure stability (LO 1.3.5).

The Rules for Electron Filling

1. The Aufbau Principle (German for "building up"): Electrons occupy the lowest energy levels first (as listed above).
2. The Pauli Exclusion Principle: An orbital can hold a maximum of two electrons, and these electrons must have opposite spin. This minimizes repulsion. We represent opposite spins using arrows, one pointing up (\(\uparrow\)) and one pointing down (\(\downarrow\)).
3. Hund's Rule (Rule of Maximum Multiplicity): When filling orbitals within the same sub-shell (like \(p_x\), \(p_y\), and \(p_z\)), electrons fill them singly first before any pairing occurs. Analogy: Imagine three empty seats on a bus; you take a single seat before sitting next to a stranger! This rule minimizes inter-electron repulsion between electrons in the same sub-shell.

Notation Methods (LO 1.3.6, 1.3.7)

There are two main ways to write configurations:

1. Full Electronic Configuration (Superscript Notation)

This shows all the filled sub-shells. The superscript number is the quantity of electrons in that sub-shell.

• Example: Oxygen (Z=8)
  \(1s^2 2s^2 2p^4\)
• Example: Potassium (Z=19)
  \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\)

2. Shorthand (Noble Gas Core) Configuration

To save time, we use the noble gas (Group 18 element) from the previous period to represent the filled inner shells.

• Example: Potassium (Z=19)
  The previous noble gas is Argon (Ar, Z=18). So, we write:
  \([Ar] 4s^1\)

3. Electrons-in-Boxes Notation (LO 1.3.7)

This notation is essential for demonstrating Hund’s Rule and showing unpaired electrons. Boxes represent orbitals, and arrows represent electrons (with their spin).

• Example: Oxygen (Z=8)
  \(1s: \uparrow\downarrow\)   \(2s: \uparrow\downarrow\)   \(2p_x: \uparrow\)   \(2p_y: \uparrow\)   \(2p_z: \uparrow\downarrow\) (Two unpaired electrons)

Special Case: Transition Elements (LO 1.3.6, 1.3.7)

We only need to consider elements up to Krypton (Z=36). Transition elements (like Iron, Fe, Z=26) involve the d orbitals.

• Example: Iron atom (Fe, Z=26)
  Configuration (using the energy filling order 4s before 3d):
  \([Ar] 3d^6 4s^2\)
• Box Notation for Iron: The 4s orbitals fill first, then the 3d orbitals apply Hund's rule.

  \([Ar]\)   \(3d: \uparrow\downarrow \uparrow \uparrow \uparrow \uparrow\)   \(4s: \uparrow\downarrow\)

  (Note the four unpaired electrons in the 3d orbitals.)

Writing Configurations for Ions (LO 1.3.6)

When an atom forms an ion, electrons are added (for negative ions) or removed (for positive ions).

The Golden Rule for Cations (Positive Ions):

Electrons are always removed from the orbital with the highest Principal Quantum Number (\(n\)) first.

• Example: Iron(II) ion (Fe²⁺)
• Start with the neutral atom: \([Ar] 3d^6 4s^2\)
• Remove 2 electrons. The highest \(n\) is \(4\), so the 2 electrons are removed from the \(4s\) orbital.
• Configuration for Fe²⁺:
  \([Ar] 3d^6 4s^0\) or simply \([Ar] 3d^6\)

Common Mistake Alert: Students often remove electrons from the 3d shell because it's written last. Always check \(n\) first!

5. Free Radicals (LO 1.3.9)

You will encounter these highly reactive species in organic chemistry reactions (like substitution reactions in alkanes).

Definition of a Free Radical

A free radical is a species (atom, ion, or molecule) that contains one or more unpaired electrons in its outer shell.

• Free radicals are often formed when a covalent bond breaks equally (homolytic fission), with one electron going to each fragment.
• Because they have an unpaired electron, they are extremely unstable and highly reactive, trying instantly to pair up that lone electron.
• Example: The Chlorine Free Radical (\(\text{Cl}\cdot\))
  This is a chlorine atom with 7 valence electrons, one of which is unpaired.

SUMMARY: Electrons, Orbitals, and Configuration

To successfully tackle problems in this chapter, always approach them in this sequence:

1. Determine the number of electrons (Z or Z minus/plus charge).
2. Follow the Aufbau Principle and the energy order (1s... 4s, 3d, 4p).
3. Apply the Pauli Exclusion Principle (max 2 e- per orbital, opposite spin).
4. Apply Hund's Rule (fill orbitals of equal energy singly first).
5. If dealing with an ion, remove/add electrons correctly (highest \(n\) first for cations).