Physics › Nuclear physics › Rutherford scattering and the nuclear atom

Rutherford scattering and the nuclear atom

Most alpha particles fired at gold foil passed straight through, showing that most of an atom is empty space, and the rare ones that bounced back implied a nucleus ten thousand times smaller than the atom around it. The radiations that nucleus emits can each be identified with paper, aluminium and lead.

Year 13AQA 3.8.1.1, 3.8.1.2 CIE 11.1.1, 11.1.7 OCR A 6.4.1(a), 6.4.1(c), 6.4.3(b)(i), 6.4.3(b)(ii)EDEXCEL 2, 6, 131, 168, 169

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 a simple absorption experiment, and give the composition, mass and charge of each, both signs of beta included.
Match each radiation to its applications and to the hazard it presents.
Use the inverse-square law for gamma with corrected count rates, as in required practical 12.

COMMON MISCONCEPTION

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

The alpha scattering experiment

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 throughout the 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 almost straight back the way it came. In the real experiment about one in eight thousand deflected through more than ninety degrees, the near-head-on returns rarer still, 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 arrived the same way. A new probe, a surprise in the data, a revised picture. That is the pattern you are asked to appreciate.

Three radiations, three absorption tests

Unstable nuclei emit three kinds of radiation, 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; whatever passes both and only thins through thick lead is gamma.

	α	β⁻	β⁺	γ
composition	2 protons and 2 neutrons: a helium nucleus	an electron	a positron	a photon, with no rest mass
mass	4u	u/1840	u/1840	zero
charge	+2e	−1e	+1e	0
stopped by	a sheet of paper	a few mm of aluminium	a few mm of aluminium, if it survives that far	thick lead, attenuating rather than halting it
ionising power	intense	moderate	moderate	weak

Read the mass row in atomic mass units, u being 1.66 × 10⁻²⁷ kg, near enough the mass of one nucleon. An alpha is 4u, or 6.6 × 10⁻²⁷ kg. A beta particle of either sign is about u/1840, or 9.1 × 10⁻³¹ kg, some seven thousand times lighter than an alpha. A gamma photon has no mass at all, and no charge either.

Beta comes in two signs, which is why the table carries two columns for it. A β⁻ particle is a fast electron and a β⁺ particle is a fast positron, identical in mass and opposite in charge, so the absorption test cannot tell them apart: a few millimetres of aluminium stops either. A magnetic field can, since it bends them opposite ways. In practice a positron gets nowhere at all in matter. Within a millimetre or two it meets an electron and annihilates, and what leaves the material is a pair of gamma photons, which is the basis of the PET scanner in the medical physics unit.

FIG. 2The absorption test: alpha stopped by paper, beta by a few millimetres of aluminium, and gamma strongly attenuated by thick lead rather than stopped outright.

Penetration and ionisation trade off against each other. Alpha is heavy, doubly charged and slow, so it ionises intensely and exhausts itself within a few centimetres of air. Outside the body that usually makes it a low hazard to intact skin, though eyes and open wounds still need care; swallowed or inhaled, an alpha emitter delivers all of that intense ionisation directly into living tissue, so internal contamination is treated as a serious hazard, with the actual risk depending on the activity, the energy and where the material lodges. Gamma penetrates furthest and ionises least.

Industry uses that range of penetrations. A beta source above a rolling sheet of paper or aluminium foil monitors the thickness from the count rate below, while steel plate needs gamma to get through at all.

Gamma also behaves differently in kind. Alpha and beta have a definite range and simply run out, while a gamma beam is attenuated, its intensity falling by a fixed fraction for each further thickness of absorber. Enough lead brings it down to whatever level a job requires, and no single thickness switches it off cleanly.

GUIDED PRACTICE

Name that radiation

A source's count rate is unchanged by a sheet of paper but falls almost to background behind 3 mm of aluminium. Identify the radiation, reasoning from the absorption tests.

Show the working

Paper stops alpha, so the unchanged rate through paper rules alpha out. Aluminium of a few millimetres stops beta but barely dents gamma.

The near-total loss behind aluminium therefore identifies beta. Absorber questions work by elimination, with each absorber answering one yes-or-no question about the radiation.

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 = \frac{k}{x^{2}}

ON THE AQA 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; treble it and a ninth remains. Increasing the distance is the simplest protection there is. Stepping back from a source, or handling it on 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, since the law describes the source's own 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.

WORKED EXAMPLE

Background first, law second

A gamma detector reads 500 counts per minute at 0.20 m from a source, and the background alone is 20 counts per minute. Predict the reading at 0.40 m.

Correct before you calculate. The source's own rate is 500 − 20 = 480 counts per minute.

Doubling the distance quarters the corrected rate, so 480/4 = 120.

Add the background back to predict what the meter will show, 120 + 20 = 140 counts per minute. Both background steps are needed: subtract before scaling, then add the background back for the predicted reading.

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, medical procedures. Measure it with the source locked away, then remove it from every reading before any analysis begins.

Medicine uses radiation with the risks assessed. 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 judgement asked for is exactly that. Name the risk, name the benefit, and argue the balance for the case in front of you. A blanket verdict that radiation is safe or dangerous answers a different, easier question than the one asked.

ASSESSMENT FOCUS

Scattering answers pair evidence with conclusion. Most alphas undeflected means mostly empty space, and a tiny fraction rebounding means 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. Give the test, then the verdict.
Describing a radiation means three properties, not one. Composition, mass and charge: two protons and two neutrons at 4u and +2e for an alpha, an electron at about u/1840 and −1e for β⁻, a positron of the same mass at +1e for β⁺, and a photon with no mass and no charge for gamma. Leaving β⁺ out of the list is the omission the question is testing for.
Correct every count rate before you use I = k/x², taking measured minus background. Arithmetic on raw counts is the classic dropped mark in RP12.
Quarter and ninth are worth quoting cold. Double the distance for a quarter of the intensity, treble it for a ninth. State the factor before you reach for a calculator.
For hazards, match the radiation to the situation. Alpha is the danger inside the body, and gamma is 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 further than 0.50 m is 1.50 m, and what does the square of that factor 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, so the atom is nearly all empty space.

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

Subtract the background before any count rate does any work.

WORKBOOK

Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.

18 questions on this topicAnswer them one at a time and mark yourself against the mark scheme.Practise this topic

Or read them with their mark schemes on the rutherford scattering and the nuclear atom questions page.

7 flashcards on this topicDefinitions, off-sheet equations and a spot-the-error card, scheduled by spaced repetition in your browser.Revise with flashcards

WHERE TO GO NEXT

Required practical 12: the inverse-square law for gamma radiation puts this topic in the lab, and the written papers ask about it.

CHECK YOUR PROGRESS

Rate how confident you feel with each objective for this lesson. Ratings are saved in this browser, on this device, unless you sign in.

Describe the alpha scattering results, and argue from them to a small, massive, positive nucleus.
Identify alpha, beta and gamma from a simple absorption experiment, and give the composition, mass and charge of each, both signs of beta included.
Match each radiation to its applications and to the hazard it presents.
Use the inverse-square law for gamma with corrected count rates, as in required practical 12.

Open the full revision checklist to track your progress across the whole unit.