What is the Nuclear Model of an atom in the context of Cambridge IGCSE Physics?

The Nuclear Model of an atom, as studied in Cambridge IGCSE Physics, describes the atom as having a small, dense nucleus at its center, composed of protons and neutrons, with electrons orbiting around this nucleus. This model was proposed by Ernest Rutherford following his gold foil experiment, which demonstrated that atoms have a concentrated positive charge at their core.

How did Rutherford's gold foil experiment lead to the development of the Nuclear Model?

Rutherford's gold foil experiment involved firing alpha particles at a thin sheet of gold foil. Most particles passed through, but some were deflected at large angles. This led Rutherford to conclude that atoms have a small, dense, positively charged nucleus, which repelled the alpha particles, thus forming the basis of the Nuclear Model of the atom.

What are the key differences between the Nuclear Model and the earlier Plum Pudding Model?

The Plum Pudding Model, proposed by J.J. Thomson, suggested that atoms were composed of electrons scattered within a 'soup' of positive charge. In contrast, the Nuclear Model, introduced by Rutherford, posits that the atom has a dense nucleus containing protons and neutrons, with electrons orbiting this nucleus, thus providing a more accurate representation of atomic structure.

Why is the Nuclear Model important in understanding atomic structure in Nuclear Physics?

The Nuclear Model is crucial in Nuclear Physics as it provides a foundation for understanding atomic structure, nuclear reactions, and the forces at play within the nucleus. It explains phenomena such as radioactivity and nuclear fission, which are key topics in the Cambridge IGCSE Physics curriculum.

How does the Nuclear Model explain the stability of atoms?

The Nuclear Model explains atomic stability through the balance of forces within the nucleus. Protons and neutrons are held together by the strong nuclear force, which overcomes the electrostatic repulsion between protons. This model helps explain why certain isotopes are stable while others are radioactive, a concept explored in Nuclear Physics at the Cambridge IGCSE level.

Why is "Saying mass number = number of protons" a common mistake in The Nuclear Model of an atom?

Why it happens: Confusing A with Z. How to avoid it: A = protons + neutrons. Z = protons only. Source: 0625/42 — recurring

Why is "Saying isotopes have different chemical properties" a common mistake in The Nuclear Model of an atom?

Why it happens: Confusing chemistry with physics. How to avoid it: Isotopes have IDENTICAL chemical properties (same electrons). Only nuclear properties differ.

Why is "Placing electrons in the nucleus" a common mistake in The Nuclear Model of an atom?

Why it happens: Forgetting the model. How to avoid it: Nucleus = protons + neutrons. Electrons orbit OUTSIDE.

Why is "Saying Rutherford proved the atom has electrons" a common mistake in The Nuclear Model of an atom?

Why it happens: Mixing experiments. How to avoid it: Rutherford showed the NUCLEUS exists. Thomson's earlier work discovered the electron.

Nuclear PhysicsCambridge IGCSE Physics (0625)

The Nuclear Model of an atom

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The Nuclear Model of an Atom — Cambridge IGCSE 0625 Physics Extended (2026)

Rutherford's gold-foil experiment, the modern picture of a tiny dense nucleus, plus proton number, nucleon number and isotope notation.

What you’ll learn

Mapped to the Cambridge IGCSE 0625 syllabus (2026-2028).

5.1 — Describe the Rutherford alpha-scattering experiment.
5.1 — Describe the structure of the atom in terms of protons, neutrons and electrons.
5.1 — Use proton number, nucleon number and isotope notation.

Rutherford's gold-foil experiment

Alpha particles fired at thin gold foil. Most pass straight through; a few bounce back. Reveals the nucleus.

Setup. A beam of alpha particles fired at very thin gold foil in a vacuum. A fluorescent screen detects where the alpha particles land.

Observations.

Most alpha particles pass STRAIGHT through, undeflected.
A small fraction are deflected at small angles.
A tiny fraction (~1 in 8000) bounce back nearly straight.

Conclusions.

Observation	Conclusion
Most pass through	Atom is mostly EMPTY space
Some deflected	Centre of atom has CONCENTRATED positive charge
A few bounced back	The positive charge is in a TINY, DENSE region — the nucleus

Before Rutherford. The "plum pudding" model imagined positive charge spread evenly with electrons embedded — alpha particles should have passed through with only minor scattering. The bounce-backs falsified that model.

Worked qualitative. Why use thin gold foil specifically?

Gold: malleable, can be hammered very thin (a few atoms thick).
Thin: most alphas only pass through one layer of nuclei.
Heavy nucleus: enough mass to deflect alphas.

Most $\alpha$ pass through → atom is mostly empty.
Few deflected → positive nucleus.
Tiny fraction bounce back → nucleus is DENSE and SMALL.
Disproved the plum-pudding model.

The modern atom

Tiny positive nucleus (protons + neutrons) with electrons orbiting in shells.

Nucleus. At the centre. Contains:

Protons ( $+1$ charge, mass $\approx 1\,\text{u}$ ).
Neutrons ( $0$ charge, mass $\approx 1\,\text{u}$ ).

Together, protons + neutrons = nucleons.

Electrons. Orbit at relatively huge distances from the nucleus, in shells.

Charge: $-1$ .
Mass: $\sim 1/1836\,\text{u}$ (much lighter than nucleons).

Sizes (rough).

Atom: $\sim 10^{-10}\,\text{m}$ .
Nucleus: $\sim 10^{-15}\,\text{m}$ — about $10^{5}$ times smaller.

Charge. A neutral atom has equal numbers of protons and electrons. An ION is an atom that has gained or lost electrons (so charge is non-zero).

Notation. $^{A}_{Z}\text{X},$ where $X$ is the element symbol, $Z$ is the proton number (atomic number), $A$ is the nucleon number (mass number).

Worked. $^{12}_{6}\text{C}$ (carbon-12).

$Z = 6$ → $6$ protons. Therefore $6$ electrons (neutral atom).
$A = 12$ → $12$ nucleons. Neutrons = $12 - 6 = 6$ .

Nucleus = protons + neutrons.
Electrons orbit in shells far from nucleus.
Atom mostly empty space.
$^{A}_{Z}\text{X}$ : $Z$ protons, $A$ nucleons.

Isotopes

Same proton number, different nucleon number — same element, different masses.

Isotope. Different forms of the same element with:

Same number of PROTONS (so same $Z$ , same chemistry).
Different number of NEUTRONS (different $A$ ).

Examples.

Carbon: $^{12}_{6}\text{C}$ , $^{13}_{6}\text{C}$ , $^{14}_{6}\text{C}$ (all 6 protons; 6, 7, or 8 neutrons).
Hydrogen: $^{1}_{1}\text{H}$ (protium), $^{2}_{1}\text{H}$ (deuterium), $^{3}_{1}\text{H}$ (tritium).

Chemical properties are determined by ELECTRONS (which match protons in a neutral atom). So all isotopes of an element have the same chemistry.

Physical properties like mass and nuclear stability differ. Some isotopes are radioactive (e.g. $^{14}\text{C}$ , $^{3}\text{H}$ ); others are stable.

Cambridge tip. When asked "what is an isotope" — the gold-standard answer mentions BOTH: same proton number AND different nucleon number (or "different number of neutrons").

Same $Z$ , different $A$ .
Same chemistry, different mass.
Some isotopes radioactive, others stable.
Examples: $^{12}\text{C}$ vs $^{14}\text{C}$ .

How it’s examined

Atomic structure appears every Paper 2 (3-4 marks: notation, definition of isotope) and most Paper 4s (4-6 marks: explain Rutherford's experiment, calculate neutrons in a nuclide). Examiner reports flag students saying 'protons and electrons' instead of 'protons and neutrons' for nucleons.

Sources: Cambridge IGCSE Physics 0625 syllabus 2026-2028 (5.1); 0625/22 May/Jun 2024 — Q15 (Rutherford, isotopes); 0625 Examiner Reports 2022-2024. Last reviewed 2026-05-06.

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Step-by-step worked examples — The Nuclear Model of an atom

Step-by-step solutions to past-paper-style questions on the nuclear model of an atom, written exactly the way a tutor would explain them at the board.

1Use nuclide notation
Core• nuclide
Question
Find the number of protons, neutrons and electrons in $^{27}_{13}\text{Al}$ (neutral atom).
Step-by-step solution
1. Step 1
  Bottom number $Z = 13$ → protons.
2. Step 2
  Top number $A = 27$ → nucleons. Neutrons = $A - Z$ .
  $27 - 13 = 14\,\text{neutrons}$
3. Step 3
  Neutral atom → electrons = protons.
Answer
$13$ protons, $14$ neutrons, $13$ electrons.
2Identify isotopes
Core• Adapted from 0625/22 May/Jun 2024 Q19• isotope
Question
Are $^{12}_{6}\text{C}$ and $^{14}_{6}\text{C}$ isotopes? Explain.
Step-by-step solution
1. Step 1
  Same proton number ( $Z = 6$ ); different nucleon number → different neutron count.
Answer
Yes — same element (carbon), different number of neutrons.
3Rutherford scattering — what it shows
Extended• Rutherford
Question
Explain what Rutherford's $\alpha$ -particle scattering experiment demonstrated about the atom.
Step-by-step solution
1. Step 1
  Most $\alpha$ particles passed straight through → atom is mostly EMPTY space.
2. Step 2
  A small fraction was deflected at large angles → a tiny, dense, POSITIVELY-CHARGED nucleus contains most of the mass.
Answer
Atoms are mostly empty space; positive charge and most of the mass are concentrated in a tiny central nucleus.
4Charge of an ion
Core• ion
Question
An aluminium atom loses three electrons. State its charge.
Step-by-step solution
1. Step 1
  Each lost electron leaves a $+1$ overall.
  $\text{charge} = +3$
Answer
$+3$ (an $\text{Al}^{3+}$ ion).
5Composition from nuclide notation
Core• nuclide
Question
Find the number of protons, neutrons and electrons in a neutral atom of $^{238}_{92}\text{U}$ .
Step-by-step solution
1. Step 1
  Protons: $Z = 92$ .
2. Step 2
  Neutrons: $N = A - Z = 238 - 92$ .
  $N = 146$
3. Step 3
  Neutral atom → electrons = protons = $92$ .
Answer
$92$ protons, $146$ neutrons, $92$ electrons.
6Pick out the isotopes
Extended• isotope
Question
Four nuclei are given: $^{16}_{8}\text{O}$ , $^{17}_{8}\text{O}$ , $^{17}_{9}\text{F}$ , $^{18}_{8}\text{O}$ . Identify the set of three that are isotopes of the same element.
Step-by-step solution
1. Step 1
  Isotopes share the SAME proton number $Z$ . Read off $Z$ for each.
2. Step 2
  $^{16}_{8}\text{O}$ : $Z = 8$ . $^{17}_{8}\text{O}$ : $Z = 8$ . $^{17}_{9}\text{F}$ : $Z = 9$ . $^{18}_{8}\text{O}$ : $Z = 8$ .
3. Step 3
  The three with $Z = 8$ are isotopes of OXYGEN. $^{17}_{9}\text{F}$ is a different element (fluorine).
Answer
$^{16}_{8}\text{O}$ , $^{17}_{8}\text{O}$ , $^{18}_{8}\text{O}$ — all oxygen.
Examiner tip
The examiner report flags candidates often grouping nuclei by nucleon number $A$ rather than proton number $Z$ . Same element = same $Z$ .
7Write an alpha-decay equation
Extended• Adapted from 0625/42 Oct/Nov 2023 Q11• alpha decay
Question
Polonium-210, $^{210}_{84}\text{Po}$ , decays by emitting an alpha particle. Write the balanced nuclear equation and identify the daughter element using the proton number.
Step-by-step solution
1. Step 1
  Alpha particle is $^{4}_{2}\text{He}$ .
2. Step 2
  Daughter mass number $A = 210 - 4 = 206$ . Daughter proton number $Z = 84 - 2 = 82$ .
3. Step 3
  $Z = 82$ is lead, Pb.
  $^{210}_{84}\text{Po} \rightarrow {}^{206}_{82}\text{Pb} + {}^{4}_{2}\text{He}$
Answer
$^{210}_{84}\text{Po} \to {}^{206}_{82}\text{Pb} + {}^{4}_{2}\text{He}$
8Beta-minus decay equation
Extended• beta decay
Question
Strontium-90, $^{90}_{38}\text{Sr}$ , undergoes $\beta^{-}$ decay. Write the balanced nuclear equation.
Step-by-step solution
1. Step 1
  Beta-minus particle: $^{0}_{-1}\text{e}$ . Inside the nucleus a neutron has converted to a proton + emitted electron.
2. Step 2
  Mass number unchanged ( $A = 90$ ). Proton number increases by 1: $Z = 38 + 1 = 39$ (yttrium, Y).
3. Step 3
  Write the equation.
  $^{90}_{38}\text{Sr} \rightarrow {}^{90}_{39}\text{Y} + {}^{0}_{-1}\text{e}$
Answer
$^{90}_{38}\text{Sr} \to {}^{90}_{39}\text{Y} + {}^{0}_{-1}\text{e}$
9Balance check on a given decay
Extended• balance
Question
A student writes the decay $^{222}_{86}\text{Rn} \rightarrow {}^{218}_{84}\text{Po} + X$ . Identify particle $X$ and state which radiation has been emitted.
Step-by-step solution
1. Step 1
  Conserve $A$ : $222 = 218 + A_{X} \Rightarrow A_{X} = 4$ .
2. Step 2
  Conserve $Z$ : $86 = 84 + Z_{X} \Rightarrow Z_{X} = 2$ .
3. Step 3
  $X$ has $A = 4$ , $Z = 2$ → a $^{4}_{2}\text{He}$ nucleus → alpha particle.
Answer
$X = {}^{4}_{2}\text{He}$ (alpha particle). The radon nucleus has undergone alpha decay.
10Why iron has the most stable nucleus
Challenge• binding energy, stability
Question
Binding-energy-per-nucleon is plotted against nucleon number $A$ . The curve peaks around $A \approx 56$ (iron). Explain qualitatively why both very light nuclei (e.g. hydrogen → helium fusion) and very heavy nuclei (e.g. uranium fission) release energy when their nuclei move towards iron.
Step-by-step solution
1. Step 1
  Binding energy per nucleon measures how tightly each nucleon is held in the nucleus. Higher value = more stable.
2. Step 2
  Light nuclei (low $A$ ) have LOW binding energy per nucleon. FUSION combines them into heavier nuclei closer to the peak → average binding-energy-per-nucleon RISES → the difference is released as energy.
3. Step 3
  Very heavy nuclei (high $A$ ) also have lower binding energy per nucleon than iron. FISSION splits them into mid-range nuclei closer to the peak → again binding-energy-per-nucleon rises → energy released.
Answer
Both fusion (light → mid) and fission (heavy → mid) move nucleons towards the iron peak of higher binding energy per nucleon — the increase in binding energy is released as kinetic energy or radiation.
Examiner tip
The examiner report flags candidates often saying 'fusion always releases energy' — fusion only releases energy when moving TOWARDS the iron peak (i.e. starting from light nuclei). Fusing nuclei heavier than iron would absorb energy.

Key Formulae — The Nuclear Model of an atom

The formulae you need to memorise for the nuclear model of an atom on the Cambridge IGCSE 0625 paper, with every variable defined in plain English and a note on when to use it.

Nuclide notation
$^{A}_{Z}\text{X}$
$A$
nucleon (mass) number = protons + neutrons
$Z$
proton (atomic) number
When to use
Specify a particular isotope.
Number of neutrons
$N = A - Z$
When to use
Count neutrons in a nuclide.

Key Definitions and Keywords — The Nuclear Model of an atom

Definitions to memorise and the exact keywords mark schemes credit for the nuclear model of an atom answers — sharpened from recent examiner reports for the 2026 0625 sitting.

Proton
Examiner keyword
Positively charged particle in the nucleus. Charge $+e$ , mass $\approx 1\,\text{u}$ .
Neutron
Examiner keyword
Uncharged particle in the nucleus. Mass $\approx 1\,\text{u}$ .
Electron
Examiner keyword
Negatively charged particle orbiting the nucleus. Charge $-e$ , mass $\approx 1/1836\,\text{u}$ .
Isotope
Examiner keyword
Atoms of the same element (same $Z$ ) with different numbers of neutrons (different $A$ ).
Nucleon (mass) number
Examiner keyword
Total number of protons + neutrons in a nucleus. Symbol $A$ .

Common Mistakes and Misconceptions — The Nuclear Model of an atom

The traps other students keep falling into on the nuclear model of an atom questions — taken from recent Cambridge IGCSE 0625 examiner reports and mark schemes — and how to avoid them.

✕Saying mass number = number of protons
0625/42 — recurring
Why it happens
Confusing $A$ with $Z$ .
How to avoid it
$A$ = protons + neutrons. $Z$ = protons only.
✕Saying isotopes have different chemical properties
Why it happens
Confusing chemistry with physics.
How to avoid it
Isotopes have IDENTICAL chemical properties (same electrons). Only nuclear properties differ.
✕Placing electrons in the nucleus
Why it happens
Forgetting the model.
How to avoid it
Nucleus = protons + neutrons. Electrons orbit OUTSIDE.
✕Saying Rutherford proved the atom has electrons
Why it happens
Mixing experiments.
How to avoid it
Rutherford showed the NUCLEUS exists. Thomson's earlier work discovered the electron.

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The Nuclear Model of an atom — frequently asked questions

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The Nuclear Model of an atom

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Use nuclide notation

2Identify isotopes

3Rutherford scattering — what it shows

4Charge of an ion

5Composition from nuclide notation

6Pick out the isotopes

7Write an alpha-decay equation

8Beta-minus decay equation

9Balance check on a given decay

10Why iron has the most stable nucleus

Nuclide notation

Number of neutrons

Proton

Neutron

Electron

Isotope

Nucleon (mass) number

✕Saying mass number = number of protons

✕Saying isotopes have different chemical properties

✕Placing electrons in the nucleus

✕Saying Rutherford proved the atom has electrons

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

The Nuclear Model of an atom — frequently asked questions