Chemistry (9701) | Atomic structure

Study Notes: Atomic Structure (AS Level Chemistry 9701, Topic 1)

Welcome to the foundational chapter of Physical Chemistry! Atomic structure is the bedrock upon which all of chemistry is built. Understanding how atoms are put together—where the tiny particles live and how their energy levels are arranged—will make bonding, periodicity, and chemical reactions much easier to grasp. Don't worry if some concepts feel abstract; we will use analogies to make them concrete!

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1.1 Particles in the Atom and Atomic Radius

The Structure of the Atom: Mostly Empty Space

Imagine a football stadium. If the nucleus were a pea placed at the centre line, the closest electrons would be running around the perimeter fence! This analogy illustrates the key takeaway from the Rutherford scattering experiment:

• Atoms consist mainly of empty space.
• At the center is a tiny, dense core called the nucleus, which contains protons and neutrons.
• Electrons orbit this nucleus in specific energy levels called shells.

Sub-atomic Particles: Mass and Charge

Atoms are built from three fundamental particles. You must know their relative masses and charges:

Particle	Location	Relative Mass (amu)	Relative Charge
Proton (p)	Nucleus	1	+1
Neutron (n)	Nucleus	1	0 (Neutral)
Electron (e)	Shells/Orbitals	\(\frac{1}{1840}\) (Negligible)	–1

The atom's mass is concentrated almost entirely in the nucleus (protons and neutrons).
The atom's charge is governed by the number of protons (positive) and electrons (negative).

Key Terminology for Identification

You need to use these terms precisely when describing an element (X):

• Atomic Number (Z) or Proton Number: The number of protons in the nucleus. This number uniquely identifies the element. In a neutral atom, Z = number of protons = number of electrons.
• Mass Number (A) or Nucleon Number: The total number of protons and neutrons in the nucleus.
• Calculation: Number of Neutrons = \(A - Z\).

How Particles Behave in an Electric Field

When beams of these particles move through an electric field:

• Protons (positive charge) are deflected towards the negative plate.
• Electrons (negative charge) are deflected towards the positive plate. Because electrons are so much lighter (\(\approx \frac{1}{1840}\) the mass), they are deflected much more sharply than protons.
• Neutrons (no charge) are not deflected.

Analogy: Think of a magnet. Opposites attract, and the lighter object is easier to pull!

Calculating Protons, Neutrons, and Electrons in Ions

When an atom forms an ion, the number of protons and neutrons remains the same, but the number of electrons changes:

• Positive Ion (Cation): Lost electrons. Electron count = \(Z - \text{Charge}\). (e.g., \(Mg^{2+}\) lost 2 electrons).
• Negative Ion (Anion): Gained electrons. Electron count = \(Z + |\text{Charge}|\). (e.g., \(Cl^{-}\) gained 1 electron).

Trends in Atomic and Ionic Radii (Qualitative Explanation)

You must be able to state and explain the trends across a period and down a group.

Down a Group (e.g., Li \(\rightarrow\) Na \(\rightarrow\) K)

• Trend: Atomic and ionic radii increase.
• Explanation: Moving down a group, electrons are added to completely new principal quantum shells (energy levels). These outer electrons are further from the nucleus, and the increased shielding by the inner electrons reduces the effective nuclear attraction.

Across a Period (e.g., Na \(\rightarrow\) Cl)

• Trend: Atomic and ionic radii decrease.
• Explanation: Moving across a period, electrons are added to the same principal quantum shell. However, the number of protons (nuclear charge) increases steadily. This increased nuclear charge pulls the electron cloud closer to the nucleus, with minimal increase in shielding.

Key Takeaway 1.1: Atoms are defined by protons (Z). Mass is A. Electrons are in shells. Radius decreases across a period (stronger nuclear pull) and increases down a group (more electron shells).

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1.2 Isotopes

Defining Isotopes

The term isotope sounds complicated, but it just means "variations of the same element."

Definition: Isotopes are atoms of the same element (meaning they have the same number of protons, Z) but different numbers of neutrons (meaning they have different mass numbers, A).

Example: Carbon-12 (\(^{12}_{6}C\)) has 6 p and 6 n. Carbon-14 (\(^{14}_{6}C\)) has 6 p and 8 n.

Isotope Notation

The notation for an isotope is \(^{A}_{Z}X\), where:

• X is the symbol of the element.
• A (Superscript) is the Mass/Nucleon Number.
• Z (Subscript) is the Atomic/Proton Number.

Properties of Isotopes

The key differences between chemical and physical properties depend entirely on which sub-atomic particle dictates the property.

1. Chemical Properties: Same

• Why? Chemical reactions are governed by the number and arrangement of electrons (especially valence electrons). Since isotopes of the same element have the same number of protons (Z), they must have the same number of electrons (for neutral atoms). Thus, their chemical behavior is identical.

2. Physical Properties: Different

• Why? Physical properties like mass and density depend directly on the total mass of the atom. Since isotopes have different numbers of neutrons, they have different masses (A) and will therefore exhibit different physical properties (e.g., \(^{14}C\) is denser than \(^{12}C\)).

Key Takeaway 1.2: Isotopes have the same protons (same chemistry) but different neutrons (different physical properties like mass).

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1.3 Electrons, Energy Levels, and Atomic Orbitals

Electrons don't just hang out randomly; they exist in specific, organised regions.

The Electron Hierarchy (The Apartment Building Analogy)

Imagine electrons living in an apartment building:

1. Shells (Principal Quantum Number, n): These are the main floors (n = 1, 2, 3...). The higher the number, the further from the nucleus and the higher the energy.
2. Sub-shells: These are the types of apartments on each floor (s, p, d, f).
3. Orbitals: These are the individual rooms where the electrons actually live. Each orbital can hold a maximum of 2 electrons.

Orbital Capacity

• s sub-shell: Contains 1 orbital. Max 2 electrons.
• p sub-shell: Contains 3 orbitals. Max 6 electrons.
• d sub-shell: Contains 5 orbitals. Max 10 electrons.

Note: You only need to know up to the d sub-shell for AS Level.

Describing Orbital Shapes

The shape of the orbital describes the region where there is a high probability of finding an electron.

• s orbital: Always spherical. The size increases as n increases (e.g., 2s is larger than 1s).
• p orbitals: Always dumbbell-shaped. Since there are three p orbitals per sub-shell, they are oriented along the x, y, and z axes (\(p_x, p_y, p_z\)).

The Rules of Electronic Configuration

We only consider atoms and ions in their lowest energy state (the ground state). For AS Level, you only need to cover elements from Hydrogen (\(Z=1\)) up to Krypton (\(Z=36\)).

1. The Energy Order (The Filling Sequence)

The order in which sub-shells fill is based on increasing energy:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p

Crucial Point: The 4s sub-shell fills before the 3d sub-shell, even though 3 is a lower principal quantum number than 4.

2. Key Principles (Why Electrons Arrange Themselves This Way)

• Aufbau Principle: Electrons fill the lowest energy levels first.
• Pauli Exclusion Principle: An orbital can hold a maximum of two electrons, and these electrons must have opposite spins (represented by arrows pointing up and down).
• Hund's Rule of Maximum Multiplicity: When filling orbitals of equal energy (like the three p orbitals or five d orbitals), electrons occupy them singly first, before pairing up. This minimizes inter-electron repulsion.

Notations for Electronic Configurations

1. Full Electronic Configuration

Shows every sub-shell:

Example for Silicon (Z=14): \(1s^2 2s^2 2p^6 3s^2 3p^2\)

2. Shorthand (Noble Gas) Configuration

Uses the preceding noble gas symbol in square brackets:

Example for Iron (Z=26): \([Ar] 3d^6 4s^2\)

3. Electrons-in-Boxes Notation

Uses boxes for orbitals and arrows for electrons, crucial for demonstrating Hund's rule and identifying unpaired electrons.

Example for Oxygen (Z=8): \(1s^2 2s^2 2p^4\)

1s: \(\uparrow\downarrow\)   2s: \(\uparrow\downarrow\)   2p: \(\uparrow\downarrow\) \(\uparrow\) \(\uparrow\) (Hund's rule applied: two unpaired electrons)

Example for Iron (Fe, Z=26, using shorthand):

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

Free Radicals

A key term, especially in Organic Chemistry.

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

Example: The Chlorine radical, \(Cl\cdot\), has an unpaired electron, making it highly reactive.

Key Takeaway 1.3: Electrons fill 1s, 2s, 2p, 3s, 3p, 4s, 3d... Orbitals hold 2 electrons max. Remember Hund's rule for stability (unpaired before paired) and the shape difference between spherical s and dumbbell p.

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1.4 Ionisation Energy (IE)

Ionisation energy tells us how much energy is needed to remove an electron. It is a fundamental property used to explain periodicity and bonding.

Definition and Equations

Definition of First Ionisation Energy (\(IE_1\)): The energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of unipositive gaseous ions.

The phase symbols (g) are essential!

Equation for the First Ionisation Energy of Element X:

$$X(g) \rightarrow X^+(g) + e^{-}$$

Subsequent Ionisation Energies

Once the first electron is removed, you can remove a second (Second IE), a third (Third IE), and so on. They always get larger because you are removing a negative electron from an increasingly positive ion.

Second Ionisation Energy (\(IE_2\)):

$$X^+(g) \rightarrow X^{2+}(g) + e^{-}$$

Third Ionisation Energy (\(IE_3\)):

$$X^{2+}(g) \rightarrow X^{3+}(g) + e^{-}$$

Factors Influencing Ionisation Energy

The magnitude of IE depends on how strongly the outer electron is attracted to the nucleus. Four key factors are involved:

1. Nuclear Charge (Proton Number): Higher nuclear charge = stronger attraction = higher IE.
2. Atomic/Ionic Radius: Smaller radius (electron closer to nucleus) = stronger attraction = higher IE.
3. Shielding Effect: Inner electrons repel the outer electrons, "shielding" them from the full nuclear charge. More shielding = weaker attraction = lower IE.
4. Spin-Pair Repulsion: When an electron is forced to pair up in an orbital, the mutual repulsion between the two electrons makes the electron easier to remove (lower IE).

Trends in First Ionisation Energy

Down a Group (e.g., Group 1: Li \(\rightarrow\) Na \(\rightarrow\) K)

• Trend: IE decreases.
• Explanation: Both the atomic radius and shielding increase significantly due to the addition of new shells. This overcomes the slight increase in nuclear charge, making the outer electron much easier to remove.

Across a Period (e.g., Period 3: Na \(\rightarrow\) Ar)

• General Trend: IE increases.
• Explanation: The nuclear charge increases while the outer electrons are in the same shell (similar shielding). The stronger attraction pulls the electrons closer, requiring more energy to remove them.

The "Dips" (Sub-Trends)

The steady increase across a period is broken by two small dips. These provide critical evidence for sub-shells and orbitals:

1. Dip 1: Group 2 \(\rightarrow\) Group 13 (e.g., Mg \(\rightarrow\) Al)

• Observation: IE drops slightly from the element in Group 2 (ending \(s^2\)) to the element in Group 13 (starting \(p^1\)).
• Explanation: The electron being removed from the Group 13 element is in a p orbital, which is slightly higher in energy than the s orbital electrons (even though they are in the same shell, n). This electron also experiences slight extra shielding from the filled s orbital, making it easier to remove.

2. Dip 2: Group 15 \(\rightarrow\) Group 16 (e.g., P \(\rightarrow\) S)

• Observation: IE drops slightly from the element in Group 15 (ending \(p^3\)) to the element in Group 16 (starting \(p^4\)).
• Explanation: The Group 15 element has half-filled p orbitals (\(p_x^1 p_y^1 p_z^1\)), which is a relatively stable, low-repulsion configuration (Hund's rule). The Group 16 element has one p orbital with two electrons. Removing one of these paired electrons is easier due to spin-pair repulsion.

Deducing Electronic Configuration and Position from Successive Ionisation Energies

By observing the large jumps in successive IE values, you can determine which shell or sub-shell the electron was removed from.

Rule: A huge jump in IE occurs when the electron being removed comes from a new, inner, fully filled shell that is much closer to the nucleus.

Example: Element Y has the following IEs (kJ/mol):

IE1: 578   IE2: 1817   IE3: 2745   IE4: 11577

The jump occurs between IE3 and IE4 (from ~2700 to ~11500). This means the first three electrons were in the outer shell (valence shell), and the fourth electron was deep in an inner shell.

• Outer Shell Electrons = 3
• Valence Configuration: \(...s^2 p^1\)
• Conclusion: Element Y is in Group 13.

Key Takeaway 1.4: IE is the energy to remove an electron (always positive). IE increases across a period but shows dips at Group 13 (new p sub-shell) and Group 16 (spin-pair repulsion). Look for big jumps in successive IE data to find the number of valence electrons.