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The atom is the starting point for almost all of A-Level physics. Before quark substructure, particle interactions or the photoelectric effect can be discussed, students need a clear picture of what an atom is made of, how atoms of the same element differ in their nuclear composition, and how the macroscopic concept of charge per unit mass — the specific charge — connects to measurable quantities. This lesson establishes the vocabulary and arithmetic needed for everything that follows in the Particles and Radiation strand.
Specification mapping. This lesson develops AQA A-Level Physics (7408) Particles and Radiation strand, sub-strand 3.2.1.1 (constituents of the atom: proton, neutron, electron; specific charge q/m; proton number Z, nucleon number A, isotopes and nuclide notation). Refer to the official AQA 7408 specification document for the authoritative wording. The lesson is placed first in the course so that all subsequent particle-physics treatments — antiparticles, the quark substructure of protons and neutrons, conservation laws — can build on a shared atomic-structure foundation.
Synoptic links. Three immediate synoptic threads run through this content. First, nuclear stability and decay (course 6, 3.8) — the mass number A and proton number Z introduced here are the coordinates of the N–Z stability diagram, on which the stable nuclides form a curve that bends away from the N = Z line toward neutron-rich isotopes for heavier elements. Second, the quark model (our order 3, 3.2.1.6) — protons and neutrons are not fundamental; they are composite particles of three quarks each (uud and udd), so the proton-neutron arithmetic of this lesson is the macroscopic shadow of the quark-counting arithmetic of the later lessons. Third, GCSE chemistry — atomic structure and the periodic table — A-Level physics revisits this material but with much greater precision (specific charges quoted to three significant figures, neutron-rich isotopes treated as fundamentally interesting rather than as exceptions, and isotope nuclide notation taken as the standard form).
At the heart of every atom lies a tiny, dense nucleus containing protons and neutrons, surrounded at much larger distances by a cloud of electrons. Two scales make this picture concrete:
The factor of 100 000 between these two scales means that the nucleus is to the atom what a marble is to a sports stadium. Almost all of the atom's volume is essentially empty space; almost all of its mass is concentrated in the nucleus.
| Particle | Symbol | Charge (C) | Charge (e) | Mass (kg) | Mass (u) |
|---|---|---|---|---|---|
| Proton | p | +1.60 × 10⁻¹⁹ | +1 | 1.67 × 10⁻²⁷ | 1.00728 |
| Neutron | n | 0 | 0 | 1.67 × 10⁻²⁷ | 1.00867 |
| Electron | e⁻ | −1.60 × 10⁻¹⁹ | −1 | 9.11 × 10⁻³¹ | 0.000549 |
Several points are worth dwelling on. The proton charge is exactly equal in magnitude to the electron charge but opposite in sign — this is one of the most precisely tested equalities in physics, with experimental limits below one part in 10²¹. The neutron is electrically neutral but is not an internally chargeless particle: it has zero net charge but a small magnetic moment that hints at its composite (three-quark) substructure. The electron is roughly 1836 times lighter than the proton — a ratio that means electrons contribute almost nothing to atomic mass but determine almost everything about chemistry and atomic spectra.
To work with sub-microscopic masses conveniently, physicists use the unified atomic mass unit u, defined so that one carbon-12 atom has mass exactly 12 u:
1 u = 1.66 × 10⁻²⁷ kg
Proton and neutron masses are both very close to 1 u; the small differences (1.00728 u and 1.00867 u) are physically meaningful and become important in nuclear-binding-energy calculations later.
graph TD
A["Atom (~10⁻¹⁰ m)"] --> B["Nucleus (~10⁻¹⁵ m)"]
A --> C["Electron cloud"]
B --> D["Protons (+1e each)"]
B --> E["Neutrons (0 charge)"]
C --> F["Electrons (−1e each)"]
D --> G["Proton number Z = atomic number"]
D --> H["Determines element identity"]
E --> I["Neutron number N"]
D --> J["Nucleon number A = Z + N"]
E --> J
Three integers fully specify any nucleus:
| Symbol | Name | Definition |
|---|---|---|
| Z | Proton number (atomic number) | Number of protons in the nucleus |
| N | Neutron number | Number of neutrons in the nucleus |
| A | Nucleon number (mass number) | Total protons + neutrons (A = Z + N) |
The proton number Z fixes the element. Two atoms with the same Z but different N are still the same chemical element — they only differ in nuclear mass and stability.
A specific nucleus is written using nuclide notation:
ᴬ_Z X
where X is the chemical symbol of the element, A is the nucleon number (top-left), and Z is the proton number (bottom-left). Examples:
| Nuclide | Element | Z | N | A |
|---|---|---|---|---|
| ¹_₁H | Hydrogen-1 (protium) | 1 | 0 | 1 |
| ²_₁H | Hydrogen-2 (deuterium) | 1 | 1 | 2 |
| ³_₁H | Hydrogen-3 (tritium) | 1 | 2 | 3 |
| ¹²_₆C | Carbon-12 | 6 | 6 | 12 |
| ¹⁴_₆C | Carbon-14 | 6 | 8 | 14 |
| ²³⁵_₉₂U | Uranium-235 | 92 | 143 | 235 |
| ²³⁸_₉₂U | Uranium-238 | 92 | 146 | 238 |
The Z subscript is technically redundant (it is fixed by the element symbol) but writing it explicitly makes conservation arithmetic in decay equations much cleaner.
Isotopes are nuclei of the same element with the same Z but different N — and therefore different A. Almost every element occurs naturally as a mixture of isotopes. The chemical properties of isotopes are virtually identical because chemistry is determined by electrons (and hence by Z), but the nuclear properties — masses, stability, decay modes — can differ dramatically.
A nucleus contains 17 protons and 20 neutrons. What is it?
Compare ²³⁵_₉₂U and ²³⁸_₉₂U. How many protons and neutrons does each contain?
The three extra neutrons in ²³⁸U make it non-fissile and roughly 7 × 10⁸ years more stable (its half-life is 4.5 × 10⁹ years against 7 × 10⁸ years for ²³⁵U).
The strong nuclear force is short-range (~1 fm) and attractive between any pair of nucleons (proton-proton, proton-neutron, neutron-neutron); the electromagnetic force is long-range and repulsive between proton pairs. For light nuclei, equal numbers of protons and neutrons (N ≈ Z) optimise the strong-force binding without excessive electromagnetic repulsion. For heavier nuclei, more neutrons are needed to "dilute" the proton-proton repulsion — hence the bending of the stability line toward neutron-rich compositions at high Z. This is treated in detail in the nuclear-physics course; for now, just note that for a given Z, only a few values of N produce a stable nucleus.
The specific charge of a particle is its charge per unit mass:
Specific charge = Q / m
with SI units of coulombs per kilogram (C kg⁻¹).
Specific charge is the quantity that determines how a charged particle responds to electric and magnetic fields — exactly the quantity measured by J. J. Thomson in his 1897 cathode-ray-tube experiment that first identified the electron as a distinct subatomic particle.
| Particle | Charge (C) | Mass (kg) | Specific charge (C kg⁻¹) |
|---|---|---|---|
| Electron | −1.60 × 10⁻¹⁹ | 9.11 × 10⁻³¹ | −1.76 × 10¹¹ |
| Proton | +1.60 × 10⁻¹⁹ | 1.67 × 10⁻²⁷ | +9.58 × 10⁷ |
| Neutron | 0 | 1.67 × 10⁻²⁷ | 0 |
Two observations:
For composite objects like nuclei, ions and atoms, the specific charge is the total charge divided by the total mass.
An alpha particle is a helium-4 nucleus, ⁴_₂He²⁺. It contains 2 protons and 2 neutrons. Calculate its specific charge.
Comparison: the alpha particle's specific charge is roughly half that of the proton, because it has twice the charge but four times the mass.
A bare ²³⁵U nucleus has 92 protons and 143 neutrons. Calculate its specific charge (treating proton and neutron masses as equal to 1.67 × 10⁻²⁷ kg).
The ²³⁵U nucleus has a smaller specific charge than the alpha particle because its charge-to-mass ratio is reduced by the neutron content.
Place the following in order of decreasing specific charge: electron, proton, alpha particle, ²³⁵U nucleus, neutron.
From the values above:
The electron's specific charge is roughly 1800 times larger than even the proton's — this is why electrons are so easy to accelerate to high speeds with modest potential differences, while protons require correspondingly larger fields. The fact that the electron's specific charge exceeded any expectation from chemistry was Thomson's key clue that the electron was a new type of particle, not just a small charged ion.
When an atom gains or loses one or more electrons, it becomes a charged ion:
The nuclear charge Z does not change in ionisation — only the electron count.
A doubly ionised helium atom is the same particle as the alpha particle (He²⁺ — both have 2 protons, 2 neutrons, and no electrons). What is the specific charge of a singly ionised helium atom He⁺?
He⁺ has 2 protons, 2 neutrons and 1 electron.
Half that of the alpha particle, because the charge has been halved (one fewer net positive elementary charge), while the mass is essentially unchanged.
A bare ¹²C nucleus contains 6 protons and 6 neutrons. Calculate its specific charge.
Coincidentally equal to that of the alpha particle (both have charge-to-mass ratios of about 0.5 in units of e per nucleon, since carbon-12 has Z = 6 and A = 12, while helium-4 has Z = 2 and A = 4 — both give Z/A = 0.5).
A natural follow-up question after introducing isotopes is: which isotopes are stable? The answer involves the interplay of two competing forces:
For light nuclei (Z up to about 20), the strong force is best balanced by approximately equal numbers of protons and neutrons (N ≈ Z). For heavier nuclei, more neutrons are needed to dilute the electromagnetic repulsion, so the stability line bends to N > Z. Beyond Z = 82 (lead), no stable nuclei exist at all — every heavier nucleus decays eventually, with half-lives ranging from microseconds to billions of years. The mechanisms of decay (α, β⁻, β⁺) and the role of the weak interaction in beta decay are developed in detail in the nuclear physics course (3.8) of the AQA specification.
Specimen question modelled on the AQA paper format (6 marks).
(a) State the constituents of a ²⁷_₁₃Al nucleus. [2 marks]
(b) Calculate the specific charge of a singly ionised ²⁷_₁₃Al⁺ ion, giving your answer in C kg⁻¹ to three significant figures. Take the proton and neutron masses as 1.67 × 10⁻²⁷ kg and the electron mass as 9.11 × 10⁻³¹ kg. [3 marks]
(c) Explain how the specific charge of ²⁷_₁₃Al⁺ would compare with that of ²⁶_₁₃Al⁺ (an isotope of aluminium). [1 mark]
For this 6-mark item, AO1 (knowledge) carries 2 marks for recalling the structure of a nucleus and the definition of specific charge. AO2 (application) carries 3 marks for substituting numerical values correctly and computing the specific charge of a specific ion. AO3 (evaluation) carries 1 mark for the comparative reasoning in part (c). Examiners reward explicit working in part (b); a single numerical answer without intermediate substitution typically earns at most half-credit even if the final value is correct.
Grade C response (4 marks out of 6).
(a) 13 protons and 14 neutrons in the nucleus, plus 13 electrons (in a neutral atom).
(b) Charge of Al⁺ = +e = 1.60 × 10⁻¹⁹ C. Mass ≈ 27 × 1.67 × 10⁻²⁷ = 4.51 × 10⁻²⁶ kg. Specific charge = 1.60 × 10⁻¹⁹ / 4.51 × 10⁻²⁶ = 3.55 × 10⁶ C kg⁻¹.
(c) ²⁶Al⁺ has the same charge but smaller mass so the specific charge is bigger.
Examiner commentary: Part (a) earns 2/2 — though the question asks specifically about the nucleus, the candidate has correctly identified the nucleus constituents and then added the (correct but unrequested) electron information. Part (b) earns 2/3 — correct method and final answer, but the mass calculation does not explicitly subtract the missing electron's mass nor add the 12 remaining electrons' contribution; the candidate has essentially treated the ion as a bare nucleus, which is the standard A-Level approximation but the working should state that the electron mass is negligible compared with the nucleon mass. Part (c) earns 1/1 — correct direction (smaller mass → larger specific charge). A solid Grade C response.
Grade A response (6 marks out of 6).*
(a) The ²⁷_₁₃Al nucleus contains 13 protons (from Z = 13) and 27 − 13 = 14 neutrons.
(b) An Al⁺ ion has lost one electron, so the net charge of the ion is +1e = +1.60 × 10⁻¹⁹ C.
Mass of the ion = (mass of 13 protons) + (mass of 14 neutrons) + (mass of 12 remaining electrons) ≈ 27 × 1.67 × 10⁻²⁷ + 12 × 9.11 × 10⁻³¹ = 4.509 × 10⁻²⁶ + 1.09 × 10⁻²⁹ ≈ 4.51 × 10⁻²⁶ kg (the electron contribution is approximately 0.024% — negligible to three significant figures).
Specific charge = Q / m = 1.60 × 10⁻¹⁹ / 4.51 × 10⁻²⁶ = 3.55 × 10⁶ C kg⁻¹.
(c) ²⁶_₁₃Al⁺ has one fewer neutron (mass smaller by about 1.67 × 10⁻²⁷ kg = ~3.7%) but the same net charge of +e. The specific charge is therefore larger for ²⁶Al⁺, by approximately 1/26 ≈ 3.8% compared with ²⁷Al⁺. Numerically, the specific charge of ²⁶Al⁺ would be approximately 3.55 × 10⁶ × (27/26) ≈ 3.69 × 10⁶ C kg⁻¹.
Examiner commentary: Full 6/6. Part (a) earns 2/2 with explicit derivation of N from A − Z. Part (b) earns 3/3 with full substitution, explicit consideration (and dismissal) of the electron mass contribution, and a final answer correctly stated to three significant figures with units. Part (c) earns 1/1 with quantitative reasoning (the ~3.7% mass change predicts a ~3.8% specific-charge change) rather than just stating "larger". The A* differentiator is the explicit consideration of the electron mass and the quantitative comparison in (c).
A common error in nuclide-notation questions is to confuse A and Z. The top number is A (total nucleons); the bottom is Z (protons only). The mnemonic "Above is All; below is Bottom-protons" helps some students.
Many candidates add the electron mass when calculating specific charges of bare nuclei. For a bare nucleus, there are no electrons; for an ion, only the remaining electrons (Z − n for an n-fold positive ion) contribute. The electron contribution is typically less than 0.1% of the total mass and is justifiably neglected at A-Level, but you should state the approximation.
A subtle error is to treat protons and neutrons as having identical masses. They are very close (within 0.14%) but the small mass difference (m_n − m_p ≈ 2.3 × 10⁻³⁰ kg) becomes important in beta-decay energy calculations. At A-Level for specific-charge questions, using a single nucleon mass is acceptable.
Many candidates lose marks by omitting units on specific-charge answers. C kg⁻¹ (coulombs per kilogram) is the only correct SI form.
A predictable confusion is between isotopes (same Z, different N) and isobars (same A, different Z). Isobars are not in the A-Level core but turn up in synoptic nuclear-physics questions.
The discovery of the nucleus itself is one of the most famous experiments in physics. In 1909–11, Geiger and Marsden (working in Rutherford's lab in Manchester) fired alpha particles at thin gold foil and observed that a small but significant fraction were deflected through very large angles — some even backward. Rutherford's interpretation, published in 1911, was that the atom's positive charge and most of its mass must be concentrated in a tiny central nucleus, with the rest of the atom essentially empty space. The famous remark — that the result was as surprising as a 15-inch shell bouncing back off a sheet of tissue paper — captures how radically the result overturned the then-current "plum pudding" model.
The discovery of the neutron came much later, in 1932, by James Chadwick in Cambridge. Chadwick fired alpha particles at beryllium and observed a penetrating, uncharged radiation that could knock protons out of paraffin wax with high energy. The penetrating particles were eventually identified as neutrons — equal in mass to protons but electrically neutral. Chadwick won the 1935 Nobel Prize.
For sixth-formers considering physics at university, the CERN Open Data Portal publishes real LHC datasets that students can analyse to "discover" particles in real collision events. The book "The Particle at the End of the Universe" by Sean Carroll is an accessible recent introduction to the Standard Model with emphasis on the 2012 Higgs discovery.
At the A*/A boundary, three subtleties separate confident answers from confused ones. First, students often write "the atom is mostly empty space" without qualification. More precisely: the volume of the atom is mostly empty space (the nucleus occupies about 10⁻¹⁵ of the atom's volume), but the probability density of the electron cloud is non-zero everywhere — it just falls off rapidly with distance from the nucleus. Treating the atom as a solid sphere is the GCSE picture; at A-Level, the electron cloud is a quantum-probabilistic object.
Second, students sometimes treat isotopes as chemically distinct. They are not — chemical reactions depend only on electron configurations, which depend only on Z. The exception is the isotope effect in reaction rates (heavier isotopes react more slowly in certain reactions), which is a small kinetic effect, not a thermodynamic one. ¹⁴C and ¹²C take part in identical biochemistry, which is why ¹⁴C dating works.
Third, the specific charge of an electron is sometimes confused with the "charge of one mole of electrons" or with the Faraday constant (96 485 C mol⁻¹). These are different quantities. Specific charge is Q/m for a single particle, with units C kg⁻¹. The Faraday constant is Avogadro's number times the electron charge, with units C mol⁻¹.
This content is aligned with the AQA A-Level Physics (7408) specification.