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Inquiry Question 2: How is it known that atoms are made up of protons, neutrons and electrons?

Investigate and analyse the Geiger-Marsden (Rutherford) gold foil experiment and Rutherford's nuclear model of the atom, and Chadwick's discovery of the neutron

A focused answer to the HSC Physics Module 8 dot point on the structure of the atom. The Geiger-Marsden gold foil experiment, Rutherford's nuclear model replacing the plum pudding, and Chadwick's 1932 discovery of the neutron using beryllium-alpha collisions and conservation of momentum and energy.

Generated by Claude OpusReviewed by Better Tuition Academy9 min answerUpdated 2026-05-18

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What this dot point is asking

NESA wants you to describe the Geiger-Marsden gold foil experiment and Rutherford's analysis that established the nuclear atom (small dense positive nucleus, mostly empty atom), then describe Chadwick's 1932 experiment that identified the neutron as a neutral particle of nearly the proton's mass using conservation of energy and momentum. Together these experiments completed the picture of the atom as a nucleus of protons and neutrons surrounded by electrons.

The answer

Geiger-Marsden gold foil experiment (1909)

Background. Thomson's plum-pudding model (1897) had positive charge smeared diffusely over the atom with embedded electrons. To test it, Hans Geiger and Ernest Marsden (under Rutherford, at Manchester) directed a beam of alpha particles (from radium decay) at a very thin gold foil and measured how many particles scattered into different angles using a movable scintillation detector.

What they expected. Under the plum-pudding model, the smeared positive charge should produce only small Coulomb deflections. Almost all alpha particles should emerge close to the forward direction with a small spread.

What they observed.

Most alpha particles passed through with almost no deflection (consistent with mostly empty space).
A small fraction (about 1 in 8000) scattered through angles greater than 90 degrees.
A handful were back-scattered, returning toward the source.

Rutherford's interpretation. The large-angle scattering events are impossible if the positive charge is smeared over the whole atom. They require the alpha particle to encounter a strong Coulomb repulsion from a very compact positive charge. Rutherford (1911) showed that the angular distribution of scattered alpha particles is exactly what a point-like positive nucleus produces, with a $1/r^2$ Coulomb force.

Rutherford's nuclear model

The picture that emerged:

Nearly all the mass and all the positive charge of the atom is concentrated in a tiny central nucleus, with radius $\sim 10^{-15}$ m.
The atom as a whole has radius $\sim 10^{-10}$ m, so the nucleus is $10^{-5}$ of the atomic radius. The atom is mostly empty space.
Negatively charged electrons orbit the nucleus at relatively large distances.

Two open questions remained:

Why don't the orbiting electrons radiate (since accelerating charges in classical electromagnetism should radiate and spiral in)? This was solved by Bohr's 1913 quantised-orbit model, see the related dot point.
What balances the Coulomb repulsion between the protons inside the nucleus, and why does the nucleus appear to have more mass than just $Z$ protons? Both pointed to a neutral nuclear constituent.

Chadwick's discovery of the neutron (1932)

Rutherford had postulated as early as 1920 that the nucleus contained, in addition to protons, neutral particles of similar mass that he called "neutrons". The decisive evidence came from a chain of experiments.

The puzzle. Bothe and Becker (1930) observed that bombarding beryllium with alpha particles produced a highly penetrating neutral radiation that, until 1932, was assumed to be high-energy gamma rays. Curie and Joliot (1932) showed that this radiation could eject protons from paraffin wax with surprisingly high kinetic energies.

Chadwick's experiment. James Chadwick (1932) sent the neutral radiation onto various target nuclei (hydrogen, helium, lithium, nitrogen) and measured the recoil kinetic energies of each target. Using conservation of energy and momentum, he tested two hypotheses.

Hypothesis A: the neutral radiation is gamma rays. To produce the observed nitrogen recoils, the photons would have had to carry about 50 MeV of energy, far more than energetically possible from the beryllium-alpha reaction (which has an available energy of only a few MeV).
Hypothesis B: the neutral radiation is a stream of massive neutral particles. Treating the collisions as elastic billiard-ball collisions, the kinetic energies of the recoils from different targets were consistent only if the projectile had a mass close to that of the proton.

The neutron hypothesis fitted all the data. Chadwick concluded that beryllium plus alpha gives carbon plus a neutron:

^9_4\text{Be} + ^4_2\text{He} \to ^{12}_6\text{C} + ^1_0\text{n}

The neutron's mass was later measured as $1.0087$ u, slightly greater than the proton's $1.0073$ u. It has no electric charge.

Mass-and-momentum analysis (sketch)

For a head-on elastic collision of a particle of mass $m$ , speed $v_0$ , with a stationary target of mass $M$ , the target recoils with speed:

v = \frac{2 m v_0}{m + M}

Chadwick measured $v$ for hydrogen targets ( $M = 1$ u) and for nitrogen targets ( $M = 14$ u). The ratio of recoil speeds depends only on $m$ (not $v_0$ ):

\frac{v_H}{v_N} = \frac{m + 14}{m + 1}

Inserting his measured speeds and solving gave $m \approx 1$ u, confirming the neutron mass close to the proton mass.

The completed atomic picture

After Chadwick:

The nucleus contains $Z$ protons and $N$ neutrons (collectively, $A = Z + N$ nucleons).
The nucleus is held together by the strong nuclear force, which acts over very short distances and is independent of electric charge.
Electrons in number $Z$ surround the nucleus, balancing the charge in a neutral atom.

This sets the stage for the rest of Module 8: nuclear stability (binding energy), radioactive decay (alpha, beta, gamma), and ultimately the quark structure of the nucleons.

Common traps

Saying most alpha particles bounce back. Most pass through. Only a small fraction scatter through large angles, and an even smaller fraction back-scatter. That fraction is small but non-zero, and that is what was unexpected.

Calling the gold foil "thick". The foil was as thin as could be made (a few hundred atoms thick), so that most alpha particles encountered at most one nucleus.

Confusing Chadwick's neutron with a gamma ray. The whole point of his analysis was that gamma rays could not provide enough momentum given the energy available, while a massive neutral particle could.

Mixing up the radii. Atomic radius $\sim 10^{-10}$ m; nuclear radius $\sim 10^{-15}$ m. The atom is mostly empty.

Treating the nucleus as containing electrons in 1932. Before Chadwick, some models had nuclei containing protons and bound electrons to account for the extra mass and zero net charge of the neutron's role. The neutron made this unnecessary.

In one sentence

The Geiger-Marsden gold foil experiment showed that nearly all the mass and positive charge of an atom is in a tiny central nucleus (Rutherford's 1911 model), and Chadwick (1932) identified the neutron as a neutral particle of nearly the proton's mass by analysing momentum and energy conservation in alpha-beryllium collisions, completing the proton-neutron-electron picture of the atom.

Past exam questions, worked

Real questions from past NESA papers on this dot point, with our answer explainer.

2021 HSC5 marksOutline the Geiger-Marsden gold foil experiment and explain how its results led Rutherford to propose the nuclear model of the atom in place of Thomson's plum-pudding model.

Show worked answer →

Geiger and Marsden (1909, working under Rutherford) directed a beam of alpha particles from a radioactive source at a thin gold foil. A movable detector (a scintillation screen) measured the number of alpha particles scattered through different angles.

Most alpha particles passed through the foil with little or no deflection, as expected for a diffuse positive charge spread over the atom (Thomson's plum-pudding model). However, a small but non-zero fraction were deflected through very large angles, and a few were even back-scattered through more than 90 degrees.

Rutherford famously remarked that this was "as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you." The plum-pudding model could not produce such large deflections, because its smeared-out positive charge gave only small Coulomb forces on the fast alpha particles.

Rutherford (1911) concluded that the positive charge and almost all of the mass of the atom is concentrated in a tiny central nucleus, around $10^{-15}$ m in radius compared with the atom's $10^{-10}$ m. Most alpha particles pass through the (mostly empty) atom; a small fraction encounter the nucleus head-on and recoil. He worked out the angular distribution and showed it matched a $1/r^2$ Coulomb force from a point-like positive charge.

Markers reward the setup, the unexpected back-scattering, the inadequacy of the plum-pudding model, and the nuclear conclusion (small dense positive nucleus, mostly empty atom).

2019 HSC4 marksDescribe Chadwick's experiment to confirm the existence of the neutron, and explain how he distinguished neutrons from gamma rays.

Show worked answer →

Curie and Joliot (1932) showed that bombarding beryllium with alpha particles produced a neutral radiation that, in turn, ejected protons from paraffin wax. They assumed this radiation was gamma rays.

Chadwick (1932) repeated the experiment but also let the neutral radiation strike a nitrogen target and measured the recoil kinetic energy of the nitrogen nuclei. Applying conservation of energy and momentum, he found that gamma rays would have had to carry implausibly high energies (around 50 MeV) to give the observed recoils, far greater than expected for beryllium-alpha reactions.

A neutral particle of mass approximately equal to the proton, however, could give the observed proton and nitrogen recoils consistently and with reasonable energies. Chadwick concluded the radiation was a stream of neutral particles with mass close to the proton, and named them neutrons.

The reaction is:

$^9_4\text{Be} + ^4_2\text{He} \to ^{12}_6\text{C} + ^1_0\text{n}$ .

Markers reward the setup (alpha on beryllium, neutral radiation, recoil targets), the inconsistency of the gamma-ray interpretation, the conservation-of-momentum-and-energy reasoning, and the identification of the neutron with mass close to the proton.