5.10625 · Section 5: Nuclear Physics

The nuclear model of the atom

Key learnings

Atom: tiny dense nucleus, mostly empty space
The atom has a tiny, dense, positively charged nucleus holding almost all the mass, surrounded by electrons in shells; it is mostly empty space (about 1/10 000 of the atom's diameter). In the nucleus: protons (relative charge +1, mass 1) and neutrons (charge 0, mass 1). Electrons have charge −1 and negligible mass (≈ 1/1840 of a proton). A neutral atom has equal numbers of protons and electrons. Name "protons and neutrons" (not "particles") for the mark.
Nuclide notation: A top, Z bottom, N = A−Z
Atomic (proton) number $Z$ = number of protons in the nucleus; it fixes the element. Mass (nucleon) number $A$ = total protons + neutrons. Neutrons $N = A - Z$ . Nuclide notation ${}^{A}_{Z}\text{X}$ : mass number top-left, atomic number bottom-left. Example ${}^{238}_{92}\text{U}$ : $Z = 92$ protons, $N = 238 - 92 = 146$ neutrons, 92 electrons when neutral. Each definition mark needs both elements: "number of protons/nucleons in the nucleus".
Isotopes vs ions
Isotopes: atoms of the same element — same number of protons ( $Z$ ) — but a different number of neutrons (different $A$ ). Both halves are needed: e.g. ${}^{12}_{6}\text{C}$ and ${}^{14}_{6}\text{C}$ are carbon with 6 and 8 neutrons. Ions: atoms that have gained or lost electrons. A positive ion has lost electrons; a negative ion has gained electrons. Isotopes differ in neutrons; ions differ in electrons — do not confuse them.

Common mistakes

Drawn from real examiner reports.

Do not swap atomic and mass number

For ${}^{56}_{26}\text{Fe}$ some write $Z = 56$ and $A = 26$ , then get neutrons wrong. The larger number is the mass number $A$ (top-left); the smaller is the atomic number $Z$ (bottom-left). Mnemonic: "A is bigger, A is on top." Then neutrons $= A - Z = 56 - 26 = 30$ . Swapping $Z$ and $A$ is the single most common nuclear-notation error.

Nov 2023 Papers 32/33; June 2024 Paper 33 — "candidates confused the atomic number and mass number", recurring across at least 4 papers.

Isotope definition needs both halves

"Isotopes are the same element with different mass" scores zero. Cambridge needs two mark points: (1) same number of protons (same $Z$ ); (2) different number of neutrons. Naming the particle behind each difference is essential — "different mass" alone does not. Write both halves every time: same protons, different neutrons.

June 2023 Papers 31/32/33; Nov 2024 Paper 33 mark scheme explicitly requires two B marks for the isotope definition.

Positive ions lose electrons

A positive ion does NOT form by "gaining protons" or "losing neutrons". Protons and neutrons stay locked in the nucleus; only electrons transfer. A positive ion forms when a neutral atom loses electrons (fewer electrons than protons → net + charge); a negative ion forms when it gains electrons. Few candidates recall this route to a positive ion.

Nov 2023 Papers 32/33 and June 2024 Paper 33 Q10(c) — "few candidates recognised that atoms form positive ions by losing electrons".

A − Z is neutrons, not electrons

$A - Z$ gives the number of neutrons, not electrons. Some candidates think the electron count is the nucleon number minus the proton number — wrong. In a neutral atom the electron count equals $Z$ (the proton number). So neutrons $= A - Z$ ; electrons (neutral atom) $= Z$ ; keep the two subtractions apart.

November 2023 Paper 32 Q10 — examiner report: "others thought that the number of electrons was the difference between the nucleon number and the proton number".

An ion is not an isotope

An ion is not an isotope. An ion has a different number of electrons from protons (same nucleus, gained/lost electrons → charged). An isotope has a different number of neutrons (same $Z$ , same electrons, neutral). Examiners report confusion between the two: check whether the electron count or the neutron count has changed before you answer.

June 2023 Paper 31 — examiner report: "some confusion between an ion and an isotope was seen".

(E) Most alpha particles go straight through

In Rutherford scattering, most alpha particles pass straight through the gold foil (the atom is mostly empty space); only a few deflect through large angles, and very few rebound. Stating or drawing that most are deflected is wrong and misses the key evidence. The rare large-angle deflections reveal a tiny, dense, positively charged nucleus.

Exam tips

Write Z, A and N = A − Z every time
On any notation question write $Z$ , $A$ and $N = A - Z$ explicitly — do not read a number straight off the symbol. Protons $= Z$ ; neutrons $= A - Z$ (show the subtraction); electrons in a neutral atom $= Z$ . Explicit working stops you writing neutrons $= A$ by mistake.
Isotope answers: write both phrases
For isotope marks write BOTH phrases in full: "same number of protons" AND "different number of neutrons". Each is a separate B mark; one does not imply the other. "Same element, different mass" earns neither. Name the particle every time.
(E) Scattering: 3 observe-conclude pairs
Structure a Rutherford scattering answer as three observation → conclusion pairs: (1) most pass straight through → atom mostly empty space; (2) some deflect widely → concentrated positive charge; (3) a few rebound → tiny, dense, massive nucleus. Full marks need all three pairs.
Ion electrons: Z − n or Z + n
For ion electron counts start from $Z$ : a charge of $n^+$ means $Z - n$ electrons (lost $n$ ); a charge of $n^-$ means $Z + n$ electrons (gained $n$ ). Example: ${}^{40}_{20}\text{Ca}^{2+}$ has $20 - 2 = 18$ electrons. Protons and neutrons are unchanged by ionisation.

Revision notes