IMAT Chemistry · Free notes

Atomic Structure: Particles, Electrons and Radioactivity

Atomic Structure has 19 past questions since 2011, and the ministry papers from 2023 on have asked 4 of them. Most of them are counting tasks: the protons, neutrons and electrons in an atom or ion, sometimes with the mass number written in algebra, and the electron configuration that follows from the count. The ministry papers kept to short facts, such as how many electrons one orbital holds or how many valence electrons an ion has. The chemistry is simple; the marks are lost on bookkeeping, such as a charge sign read the wrong way round or a mass number used as the neutron count, so write each count down.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

5 formulas · 6 reference tables · 19 gotchas across all subtopics — the exam-eve cheat-sheet

Protons, Neutrons, Electrons and Ions

Formulas (1)

Counting protons, neutrons and electrons from a nuclide symbol · Neutrons and electrons $N = A - Z \qquad n_{e} = Z - q$

Reference tables (1)

The three subatomic particles: charge, mass and position3 rows

Particle	Relative charge	Relative mass	Where it is
Proton	+1	1	Nucleus
Neutron	0	1	Nucleus
Electron	−1	About 1/1840 (almost zero)	Shells (energy levels) around the nucleus

The proton and neutron masses are almost equal; the electron is about 1840 times lighter than either.

Watch out for (5)

Ions form by moving electrons, never protons
→ The three subatomic particles: charge, mass and position
Subtract a positive charge, add a negative one
→ Counting protons, neutrons and electrons from a nuclide symbol
The mass number is not the number of neutrons
→ Counting protons, neutrons and electrons from a nuclide symbol
Isoelectronic does not mean identical
→ Isoelectronic species: the same number of electrons
Two ions of the same element are not isoelectronic
→ Isoelectronic species: the same number of electrons

Isotopes and Relative Atomic Mass

Formulas (1)

Relative atomic mass from isotope abundances · Relative atomic mass $A_r = \frac{\sum (\text{isotope mass} \times \%\ \text{abundance})}{100}$

Reference tables (1)

Isotopes: same element, different number of neutrons7 rows

Isotope	Protons	Neutrons	Note
Hydrogen-1 (protium)	1	0	Over 99.9% of natural hydrogen; the only atom with no neutron
Hydrogen-2 (deuterium, D)	1	1	Stable; $\mathrm{D_2O}$ is heavy water
Hydrogen-3 (tritium, T)	1	2	Radioactive (beta emitter)
Carbon-12	6	6	Defines the atomic mass scale: exactly 12
Carbon-14	6	8	Radioactive; used to date once-living material
Chlorine-35	17	18	About 75% of natural chlorine
Chlorine-37	17	20	About 25% of natural chlorine

Watch out for (3)

Same mass number does not make two atoms isotopes
→ Isotopes: same element, different number of neutrons
A simple average ignores abundance
→ Relative atomic mass from isotope abundances
Relative atomic mass is per atom, not per molecule
→ Relative atomic mass from isotope abundances

Shells, Orbitals and Electron Configurations

Formulas (1)

Writing electron configurations with the Aufbau principle and Hund's rule · Order of filling $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p$

Reference tables (3)

Shells, subshells and orbitals, and how many electrons each holds4 rows

Subshell	Orbitals in it	Maximum electrons	First shell that has it
s	1	2	n = 1
p	3	6	n = 2
d	5	10	n = 3
f	7	14	n = 4

Shell 3 has 3s, 3p and 3d: 1 + 3 + 5 = 9 orbitals, so up to 18 electrons.

Quantum numbers and the Pauli exclusion principle4 rows

Quantum number	Symbol	Allowed values	What it describes
Principal	$n$	1, 2, 3, ...	The shell: energy and size
Angular momentum (azimuthal)	$l$	0 to $n - 1$ (0 = s, 1 = p, 2 = d, 3 = f)	The subshell: orbital shape
Magnetic	$m_l$	$-l$ to $+l$ , whole numbers	Which orbital: its orientation
Spin	$m_s$	$+\tfrac{1}{2}$ or $-\tfrac{1}{2}$	The direction of the electron's spin

The chromium and copper exceptions to the filling order4 rows

Element	Predicted by the filling order	Actual ground state	Why
Chromium, Z = 24	$[\mathrm{Ar}]\,3d^4\,4s^2$	$[\mathrm{Ar}]\,3d^5\,4s^1$	Half-filled 3d subshell is extra stable
Copper, Z = 29	$[\mathrm{Ar}]\,3d^9\,4s^2$	$[\mathrm{Ar}]\,3d^{10}\,4s^1$	Full 3d subshell is extra stable
Molybdenum, Z = 42	$[\mathrm{Kr}]\,4d^4\,5s^2$	$[\mathrm{Kr}]\,4d^5\,5s^1$	Same pattern as chromium (same group)
Silver, Z = 47	$[\mathrm{Kr}]\,4d^9\,5s^2$	$[\mathrm{Kr}]\,4d^{10}\,5s^1$	Same pattern as copper (same group)

Watch out for (4)

Period 3 has 8 elements, but shell 3 holds 18 electrons
→ Shells, subshells and orbitals, and how many electrons each holds
Two electrons in one orbital have opposite spins
→ Quantum numbers and the Pauli exclusion principle
4s fills before 3d
→ Writing electron configurations with the Aufbau principle and Hund's rule
Hund's rule: a p⁴ subshell has two unpaired electrons, not four
→ Writing electron configurations with the Aufbau principle and Hund's rule

Electron Configurations of Ions and Valence Electrons

Watch out for (3)

Transition metals lose 4s electrons before 3d
→ Writing the electron configuration of an ion
An anion's valence electrons are not its group number
→ Valence electrons and the outer shell of an ion
A cation with no electrons left in its old outer shell still has an outer shell
→ Valence electrons and the outer shell of an ion

Radioactive Decay, Nuclear Equations and Half-Life

Formulas (2)

Balancing nuclear equations · Conservation in a nuclear equation $\sum A_{\text{before}} = \sum A_{\text{after}} \qquad \sum Z_{\text{before}} = \sum Z_{\text{after}}$
Half-life calculations · Amount left after time t $N = N_0 \left(\tfrac{1}{2}\right)^{t/T_{1/2}}$

Reference tables (1)

Alpha, beta and gamma radiation and what each does to the nucleus4 rows

Radiation	What it is	Change to the nucleus	Charge	Stopped by
Alpha (α)	Helium nucleus ${}^{4}_{2}\mathrm{He}$ : 2 protons and 2 neutrons	A falls by 4, Z falls by 2	+2	A sheet of paper or a few cm of air
Beta-minus (β⁻)	Fast electron ${}^{0}_{-1}e$ , made when a neutron becomes a proton	A unchanged, Z rises by 1	−1	A few mm of aluminium
Beta-plus (β⁺)	Positron ${}^{0}_{+1}e$ , made when a proton becomes a neutron	A unchanged, Z falls by 1	+1	A few mm of aluminium
Gamma (γ)	High-energy electromagnetic radiation	No change to A or Z	0	Only reduced, by thick lead or concrete

Watch out for (4)

The beta electron comes from the nucleus
→ Alpha, beta and gamma radiation and what each does to the nucleus
Beta decay does not change the mass number
→ Balancing nuclear equations
Two half-lives leave a quarter, not nothing
→ Half-life calculations
Heating or reacting a sample does not change its half-life
→ Half-life calculations

PYQ weightage by concept

14 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

Protons, Neutrons, Electrons and Ions0 PYQs · 0%

Concept	PYQs	Share
The three subatomic particles: charge, mass and positionfoundation	—	—
Counting protons, neutrons and electrons from a nuclide symbolfoundation	—	—
Isoelectronic species: the same number of electronsfoundation	—	—

Isotopes and Relative Atomic Mass0 PYQs · 0%

Concept	PYQs	Share
Isotopes: same element, different number of neutronsfoundation	—	—
Relative atomic mass from isotope abundancesfoundation	—	—

Shells, Orbitals and Electron Configurations0 PYQs · 0%

Concept	PYQs	Share
Shells, subshells and orbitals, and how many electrons each holdsfoundation	—	—
Quantum numbers and the Pauli exclusion principlefoundation	—	—
Writing electron configurations with the Aufbau principle and Hund's rulefoundation	—	—
The chromium and copper exceptions to the filling orderfoundation	—	—

Electron Configurations of Ions and Valence Electrons0 PYQs · 0%

Concept	PYQs	Share
Writing the electron configuration of an ionfoundation	—	—
Valence electrons and the outer shell of an ionfoundation	—	—

Radioactive Decay, Nuclear Equations and Half-Life0 PYQs · 0%

Concept	PYQs	Share
Alpha, beta and gamma radiation and what each does to the nucleusfoundation	—	—
Balancing nuclear equationsfoundation	—	—
Half-life calculationsfoundation	—	—