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Rutherford scattering and the nuclear atom

One experiment emptied the atom: alpha particles fired at gold foil mostly sailed through, and the rare ones that bounced back revealed a nucleus ten thousand times smaller than the atom around it. The radiations that nucleus emits each carry a fingerprint you can read with paper, aluminium and lead.

Year 13AQA 3.8.1.1, 3.8.1.2CIE 11.1OCR A 6.4.1, 6.4.3

Builds on Constituents of the atom and Stable and unstable nuclei.

IN THIS TOPIC

Describe the alpha scattering results and argue from them to a small, massive, positive nucleus.
Identify alpha, beta and gamma from absorption experiments and match each to its applications and hazards.
Use the inverse-square law for gamma with corrected count rates, as in required practical 12.

WHAT YOU PROBABLY THINK

An atom is a tiny solid ball, packed with matter all the way through.

The experiment that emptied the atom

In 1909, Geiger and Marsden fired alpha particles at gold foil a few hundred atoms thick and counted where they went. If atoms were solid balls of spread-out positive charge, the plum pudding picture of the day, every alpha should have nudged through with tiny deflections. Most did. But about 1 in 8000 deflected through more than 90 degrees, and a few came almost straight back.

FIG. 1Alpha particles stream at the foil for the whole loop. Nearly every one sails straight through as though the atom were empty space, a few are nudged, and once, just once, one meets a nucleus nearly head on and comes straight back the way it came. In the real experiment that was about one in eight thousand, and it is the reason we know the atom is almost entirely empty, with its mass and positive charge packed into a tiny nucleus.

Rutherford's reading of the results still stands. Most alphas fly straight on, so most of the atom is empty space. The rare violent rebounds need a target both concentrated and heavy, so the atom's positive charge and nearly all its mass sit in a nucleus around ten thousand times smaller than the atom. The alphas that bounce back are the ones that run almost head-on into it.

The model has kept changing as the evidence has. The nucleus gained protons, then neutrons in 1932; scattering experiments later showed the proton itself has structure, the quarks you met in the particles unit. Each step came the same way: a new probe, a surprise in the data, a revised picture. That is the pattern the specification asks you to appreciate.

Three radiations, three fingerprints

Unstable nuclei emit three radiations, and a simple absorption experiment names them. Put absorbers between source and detector in turn: whatever a sheet of paper stops is alpha, whatever paper passes but a few millimetres of aluminium stops is beta, and whatever passes both, only thinning through thick lead, is gamma.

	α	β⁻	γ
nature	helium nucleus	fast electron	electromagnetic photon
charge	+2e	−1e	0
stopped by	a sheet of paper	a few mm of aluminium	thick lead, and only mostly
ionising power	intense	moderate	weak

FIG. 2The absorption test: each radiation is named by the first absorber that stops it.

Penetration and ionisation trade off. Alpha is heavy, doubly charged and slow, so it ionises intensely and exhausts itself within centimetres of air: nearly harmless outside the body, the worst of the three if swallowed or inhaled. Gamma penetrates furthest and ionises least. Industry runs on this ladder: a beta source above a rolling sheet of paper or aluminium foil monitors its thickness from the count rate below, while steel plate needs gamma to get through at all.

The inverse-square law for gamma

Gamma is the one radiation that spreads freely through air, and its intensity obeys the same geometry as light from a bulb:

I = kx²ON YOUR DATA SHEET

Double the distance from a small source and the same photons cross four times the area, so the intensity falls to a quarter; triple it and a ninth remains. This is why distance is the cheapest shielding: stepping back from a source, or handling it with long tongs, cuts the dose faster than any glove could.

FIG. 3Corrected count rate against distance: a quarter at double the distance, a ninth at triple.

Required practical 12 tests the law with a gamma source, a detector and a metre rule. Measure the count rate at a series of distances, and subtract the background count rate from every reading first: the law describes the source's photons alone. A plot of corrected count rate against 1/x² should give a straight line through the origin, the standard straightening trick for a suspected inverse square.

Background, risk and benefit

The background radiation you must subtract has ordinary origins: radon gas seeping from the ground, rocks and building materials, cosmic rays, traces in food, and medical procedures. Measure it with the source locked away, then remove it from every reading before any analysis.

Medicine uses radiation with open eyes. An X-ray or a gamma tracer carries a small, known risk of harm, weighed against the benefit of a diagnosis that may be life-saving. The specification asks for exactly that judgement: name the risk, name the benefit, and argue the balance for the case in front of you rather than declaring radiation safe or dangerous in general.

THE EXAM BIT

Scattering answers pair evidence with conclusion: most alphas undeflected so mostly empty space, a tiny fraction rebounding so a small, massive, positive nucleus. One without the other loses the mark.
In absorption questions, name the absorber that stopped the radiation, then the radiation. The examiner wants the test, then the verdict.
Correct every count rate before using I = k/x²: measured minus background. Doing arithmetic on raw counts is the classic dropped mark in RP12.
Quarter and ninth are quotable: double the distance, a quarter of the intensity; triple, a ninth. State the factor before reaching for a calculator.
For hazards, match the radiation to the situation: alpha is the danger inside the body, gamma the one that reaches you across the room.

CHECK YOURSELF

A gamma source gives a corrected count rate of 1440 counts per minute at 0.50 m. Predict the corrected count rate at 1.50 m, and explain why the background was subtracted before either reading was used.

Show a hint

How many times the distance is 1.50 m, and what does the square of that do?

Show the answer

The distance is 3 times greater, so the intensity falls by a factor of 3² = 9.

1440 / 9 = 160 counts per minute.

The inverse-square law applies to the source's own photons; background counts come from everywhere and do not fall with x, so they must be removed first.

Most alphas missed: the atom is nearly all empty space.

The rare rebounds mark a nucleus that is tiny, massive and positive.

No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.