Atomic structure: particles in the atom, isotopes, mass spectrometer, electronic configuration

Cambridge International AS & A Level Chemistry (9701) – Core Syllabus Notes

1. Particles in the Atom

An atom consists of three fundamental sub‑atomic particles. Their charge, relative mass and typical location are summarised below.

Atomic number (Z) = number of protons. In a neutral atom Z also equals the number of electrons.
Mass number (A) = protons + neutrons.

2. Isotopes & the Mass Spectrometer

2.1 Isotopes

• Atoms of the same element (same Z) that differ in neutron number (N) → different mass numbers (A).
• Notation: ⁽ᴬ⁾₍ᶻ₎X (e.g. ¹²₆C).
• Physical properties (mass, nuclear stability, radioactivity) change with A; chemical properties are essentially unchanged because they depend on Z.

2.2 Example – Carbon Isotopes

2.3 Mass Spectrometry – How Isotopic Composition Is Measured

1. Ionisation: A sample is vaporised and bombarded with electrons; atoms lose an electron to form positive ions (M⁺).
2. Acceleration & Deflection: Ions are accelerated through a known voltage and enter a magnetic field. The radius of curvature r depends on the mass‑to‑charge ratio (m/e):
   r = (m·v)/(e·B)
3. Detection: Ions of different m/e strike the detector at different positions, producing a spectrum of peaks. The relative height of each peak gives the isotopic abundance.

For a mono‑isotopic element the spectrum shows a single peak; for elements with several stable isotopes (e.g. Cl) two or more peaks appear.

3. Electronic Structure

3.1 Shells, Sub‑shells & Quantum Numbers

• Principal quantum number (n): defines the shell (n = 1, 2, 3,…).
• Azimuthal quantum number (ℓ): defines the sub‑shell; ℓ = 0, 1, 2, 3 correspond to s, p, d, f.
• Maximum electrons per sub‑shell:
  s = 2, p = 6, d = 10, f = 14.

3.2 Orbital Shapes (qualitative)

• s‑orbital – spherical.
• p‑orbitals – three mutually perpendicular dumbbells (px, py, pz).
• d‑orbitals – five clover‑shaped (plus one doughnut‑shaped) forms.
• f‑orbitals – seven complex shapes (not required for AS level).

3.3 Order of Filling – Aufbau Principle

Orbitals are filled in order of increasing n + ℓ; if two orbitals have the same n + ℓ, the one with the lower n fills first.

Sequence (first 20 orbitals):

$$1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s \dots$$

3.4 Electron‑Box (Orbital) Notation

Each box = one orbital; an arrow = one electron (↑ or ↓). Example – ground‑state carbon (Z = 6):

1s : ↑↓
2s : ↑↓
2p : ↑  ↑  (two electrons occupy two of the three 2p boxes singly – Hund’s rule)

Compact form: 1s² 2s² 2p².

3.5 Key Rules

• Pauli Exclusion Principle: No more than two electrons in an orbital and they must have opposite spins.
• Hund’s Rule: Electrons occupy separate degenerate orbitals before pairing.
• Aufbau Principle: Electrons fill the lowest‑energy orbitals first.

3.6 Free Radicals

A species with one or more unpaired electrons. Example – methyl radical:

·CH₃  Electronic configuration: 1s² 2s² 2p¹

4. Ionisation Energy (IE) & Electron Affinity (EA)

4.1 Definitions

• First ionisation energy: Energy required to remove the outermost electron from a neutral gaseous atom.
  X(g) → X⁺(g) + e⁻
• Successive IE: Energy for removing further electrons from the resulting ion.
  Xⁿ⁺(g) → X⁽ⁿ⁺¹⁾⁺(g) + e⁻
• Electron affinity: Energy change when an isolated gaseous atom gains an electron.
  X(g) + e⁻ → X⁻(g)

4.2 Periodic Trends (IE)

4.3 Example – Period 2 First IE (kJ mol⁻¹)

4.4 Using IE Data

Given IE₁ = 1314 kJ mol⁻¹ and IE₂ = 3388 kJ mol⁻¹, the values match oxygen. Hence the ground‑state configuration is 1s² 2s² 2p⁴.

4.5 Electron Affinity Trends (brief)

• Generally becomes more negative across a period (energy released) because added electron is attracted to a higher nuclear charge.
• Becomes less negative down a group due to increased radius and shielding.
• Group 17 have the most exothermic EA, but Cl’s EA is slightly more negative than F’s because of electron‑electron repulsion in the compact 2p⁶ shell.

5. Stoichiometry & the Mole

5.1 The Mole Concept

• 1 mol = 6.022 × 10²³ entities (Avogadro’s number, Nₐ).
• Molar mass (M) = relative atomic/molecular mass (g mol⁻¹).

5.2 Converting Between Mass, Moles and Particles

mass (g) = moles × M