Physics · 5 Nuclear physics

5.2.2 The three types of nuclear emission

Before you start

The nucleus contains protons (relative charge +1) and neutrons (charge 0), and electrons have relative charge −1 (5.1.2).
An atom that loses an electron becomes a positive ion (5.1.1).
Corrected count rate = measured count rate − background count rate (5.2.1).
γ-rays are the highest-frequency region of the electromagnetic spectrum (3.3).
Between oppositely charged parallel plates the electric field points from + to −, the direction of the force on a positive charge (4.2.1).
Fleming's left-hand rule for the force on a current, or on a beam of charged particles, in a magnetic field (4.5.4).
$F = m a$ and $E_{k} = \frac{1}{2} m v^{2}$ .

Syllabus objectives covered (4)

Describe the emission of radiation from a nucleus as spontaneous and random in direction
Identify alpha (α), beta (β) and gamma (γ) emissions from the nucleus by recalling: (a) their nature (b) their relative ionising effects (c) their relative penetrating abilities (β+ are not included, β-particles will be taken to refer to β–)
Describe the deflection of α-particles, β-particles and γ-radiation in electric fields and magnetic fields
Explain their relative ionising effects with reference to: (a) kinetic energy (b) electric charge

Part 1 of 7

Spontaneous and random in direction

Some nuclei are unstable. An unstable nucleus can give out radiation, and that radiation comes from the nucleus itself, not from the electrons around it. This lesson is about what the radiation is and how it behaves; 5.2.3 deals with what happens to the nucleus.
The emission is spontaneous. It happens on its own: nothing outside the nucleus triggers it. You cannot make a nucleus emit, and you cannot stop it emitting.
In particular, heating or cooling the material, putting it under pressure, or combining it into a chemical compound has no effect on the emission. Those changes act on how the atoms move and bond, which involves their outer electrons. The nucleus, deep in the centre of the atom, is not affected.
The emission is also random in direction. Each α-particle, β-particle or γ-ray leaves in a direction that cannot be predicted, and no direction is preferred over any other.
So a source sends radiation out in all directions. A detector on one side catches only the part that happens to head towards it; the rest goes elsewhere.
The timing is random too: you cannot predict when a particular nucleus will emit (5.2.3). That is why two one-minute counts from the same source usually differ slightly, and why a small difference between two counts is not evidence of anything.
In an answer, give the meaning, not just the word. Spontaneous: not caused or affected by anything outside the nucleus, such as temperature or pressure. Random in direction: each emission can go in any direction, and which direction cannot be predicted.

Part 2 of 7

What α, β and γ are

There are three kinds of emission. Two are particles of matter, with mass and charge. The third is electromagnetic radiation, with neither.
An α-particle is two protons and two neutrons bound together, which is the same as a helium nucleus. Its relative charge is +2 (two protons) and its relative mass is 4 (four nucleons). In nuclide notation:
$_{2}^{4} α or_{2}^{4} He$
A β-particle is a fast-moving electron. Its relative charge is −1 and its mass is tiny, about $\frac{1}{1840}$ of the mass of a proton. In nuclide notation the top number is 0 because its mass is so small, and the bottom number is its charge:
$_{- 1}^{0} β or_{- 1}^{0} e$
The trap here: a β-particle comes out of the nucleus, not from the electrons orbiting it. The nucleus does not hold electrons waiting to escape. The β-particle is created at the moment of emission, when a neutron changes into a proton and an electron (you meet this in 5.2.3).
γ-radiation is electromagnetic radiation of very high frequency, the γ-ray end of the spectrum from 3.3. It has no mass and no charge, and it travels at the speed of light. Its nuclide symbol is $_{0}^{0} γ$ .
Compare the two particles: an α-particle has over 7000 times the mass of a β-particle, and twice the size of charge. Keep that mass difference in mind. It explains most of what follows.
In this syllabus 'β' always means β−, the electron. The positive version, β+, is not included.

Part 3 of 7

Ionising and penetrating: opposite orders

Radiation ionises an atom when it knocks an electron out of it, leaving a positive ion. All three emissions ionise the atoms they pass through. They differ in how strongly.
Relative ionising effects: α-particles are strongly ionising, β-particles are less strongly ionising, and γ-radiation is only weakly ionising.
Penetrating ability is how much material the radiation can pass through before it is absorbed.
α-particles are stopped by a sheet of paper, and by a few centimetres of air.
β-particles pass through paper but are stopped by a few millimetres of aluminium.
γ-radiation passes through paper and aluminium. Several centimetres of lead, or a thick layer of concrete, absorbs most of it. It does not cut off sharply the way α does at paper: each extra thickness of lead lets a smaller fraction through, so say 'absorbs most' or 'greatly reduces', not 'stops completely'.
apparatus diagram — not drawn yet
Three horizontal arrows from the left labelled α, β and γ, one above the other, approaching three upright absorbers placed in a row: a sheet of paper, a few millimetres of aluminium, and a thick block of lead; the α arrow ends at the paper, the β arrow passes the paper and ends at the aluminium, the γ arrow passes paper and aluminium and continues beyond the lead as a thinner, fainter arrow.
Paper stops α, a few mm of aluminium stops β, and thick lead only reduces γ.
Put the two lists side by side. The most ionising (α) is the least penetrating, and the least ionising (γ) is the most penetrating. That is not a coincidence: ionising an atom costs the radiation energy, so radiation that ionises heavily uses up its energy in a short distance. The last section of this lesson explains this properly.
A compact way to hold all of it: α, paper; β, aluminium; γ, lead. Ionising strength runs in the opposite order.

Part 4 of 7

Identifying an emission from absorber readings

You cannot see which emission a source gives out, but you can find out by putting absorbers between the source and a detector and watching what happens to the count rate.
First measure the background count rate, with no source present. Then place the source a short distance in front of a GM tube connected to a counter: within a few centimetres, or any α-particles would be absorbed by the air before reaching the tube.
apparatus diagram — not drawn yet
A small radioactive source on the left facing a GM tube on the right, about 2 cm apart, with a gap between them labelled 'absorber (paper, aluminium or lead)'; the GM tube is connected by a lead to a counter showing a number.
Same source, same distance, change only the absorber, and compare count rates.
Record the count rate with no absorber, then with a sheet of paper, then with a few millimetres of aluminium, then with several centimetres of lead.
Read the results like this. If paper makes the count rate fall, the source emits α. If paper has no real effect but aluminium makes it fall, it emits β. If the count rate behind the aluminium is still well above background, it emits γ, and lead reducing that count confirms it.
A source can emit more than one type, so check every absorber. Do not stop at the first fall.
Because emission is random, count rates vary a little from one reading to the next. Judge 'a real fall' sensibly: 806 counts/min against 812 counts/min is no change, but 440 counts/min against 620 counts/min is a real fall.
If you are asked how much of the count rate is due to one emission, subtract the readings either side of the absorber that stops it. For γ, which none of the absorbers stops, subtract the background from the reading behind the aluminium.

Part 5 of 7

Deflection in an electric field

Recall from 4.2.1: between two oppositely charged parallel plates, the electric field points from the positive plate to the negative plate, and that is the direction of the force on a positive charge.
An α-particle is positive, so the force on it is towards the negative plate. Its path curves towards the negative plate.
A β-particle is negative, so the force on it is towards the positive plate. Its path curves the opposite way to the α-particles.
γ-radiation has no charge, so there is no force on it. It goes straight through, undeflected.
The β-particles are deflected much more than the α-particles. The α-particle has twice the charge, so the force on it is actually bigger. But it has over 7000 times the mass, and by $F = m a$ a much smaller mass gives a much bigger acceleration. So the β path bends more sharply.
forces diagram — not drawn yet
Two horizontal parallel plates, the upper labelled + and the lower labelled −, with a narrow beam entering from the left midway between them and splitting into three paths: γ continuing in a straight line, α curving gently downwards towards the − plate, and β curving sharply upwards towards the + plate.
α and β bend opposite ways; β bends far more; γ is not deflected.
Reverse the p.d. on the plates and the α and β paths swap sides. γ still goes straight through.

Part 6 of 7

Deflection in a magnetic field

A charged particle moving across a magnetic field feels a force (4.5.4). A beam of charged particles behaves like a current.
Find the direction with Fleming's left-hand rule: first finger along the field, second finger along the conventional current, and the thumb gives the force.
For α-particles, the conventional current is in the direction they travel, because they are positive.
For β-particles, the conventional current is opposite to the direction they travel, because they are negative. Point your second finger backwards along the β beam.
So α and β are deflected in opposite directions. γ-radiation has no charge and passes straight through.
The magnetic force is always at right angles to the particle's motion, so it changes the particle's direction but not its speed. Each charged beam follows an arc of a circle.
β-particles curve much more tightly than α-particles, for the same reason as in the electric field: their mass is far smaller.
forces diagram — not drawn yet
A square region filled with crosses showing a magnetic field directed into the page, with a narrow beam entering from the left and splitting into three paths: γ continuing in a straight line, α curving gently upwards along a large circular arc, and β curving sharply downwards along a small circular arc.
Field into the page, beam moving right: α curves up, β curves down and more tightly, γ goes straight on.
Check the figure with your left hand: first finger into the page, second finger pointing right (the α current), and your thumb points up the page. For β the current points left, so the force is down.
All of this assumes the field is at right angles to the beam. A charge moving along the field lines feels no force.

Part 7 of 7

Why α ionises most: charge and kinetic energy

To ionise an atom, the radiation has to pull or push an electron out of it. A charged particle does this with the electric force between its charge and the atom's electrons: an α-particle attracts them, a β-particle repels them.
Charge. The bigger the charge, the bigger the force on each electron, so the more likely an electron is to be pulled free. α has a charge of +2 and β only −1, so α ionises more strongly.
γ-radiation has no charge, so it exerts no electric force on the electrons it passes. Most γ-rays cross a great many atoms without affecting them, and only occasionally does one interact with an atom. So γ is weakly ionising.
Kinetic energy. Every ionisation takes some energy from the particle, and it comes out of the particle's kinetic energy. A particle keeps ionising only while it has kinetic energy left; when it has spent it all, it stops.
An α-particle is emitted with a large kinetic energy, usually more than a β-particle has, so it has more energy available for ionising. But its mass is so large that it moves slowly, much more slowly than a β-particle. To see why, think about $E_{k} = \frac{1}{2} m v^{2}$ : at the same speed as a β-particle, an α-particle would need over 7000 times as much kinetic energy, and its real kinetic energy is nowhere near that much bigger.
Moving slowly, the α-particle spends longer close to each atom it passes, so its large charge has longer to pull an electron free. It ionises a great many atoms on each centimetre of its path, and transfers all its kinetic energy within a few centimetres of air.
A β-particle is light, fast and has half the charge. It passes each atom quickly with a weaker pull, so it ionises far fewer atoms per centimetre. It therefore keeps its kinetic energy for much longer, which is why it travels further.
So a full explanation has two parts. The charge decides how strongly the particle pulls or pushes on electrons. The kinetic energy, and how quickly the particle gives it away, decides how many atoms it ionises in a short distance. The objective names both, so give both.

Worked examples

Example 1. A source is placed $2$ cm from a GM tube. The background count rate is $20$ counts/min. The count rates measured with different absorbers between source and tube are: no absorber, $620$ counts/min; a sheet of paper, $440$ counts/min; $3$ mm of aluminium, $140$ counts/min; $2$ cm of lead, $50$ counts/min. Deduce which emissions the source gives out, and determine the count rate due to each.

Show the working

Work through the absorbers in order, and at each one ask: did the count rate fall?
Paper: $620 \to 440$ counts/min. A fall of $180$ counts/min is far bigger than random variation, and paper stops only α-particles. So α is present.
Aluminium: $440 \to 140$ counts/min. Another large fall. These got through paper but not through aluminium, so they are β-particles. β is present.
Behind the aluminium the count rate is $140$ counts/min, far above the background of $20$ counts/min. Something passes through aluminium, and lead reduces it further to $50$ counts/min. That is γ-radiation. γ is present.
Now the count rate due to each. α is what the paper removed; β is what the aluminium removed; γ is what is left behind the aluminium once the background is taken away.
$α : 620 - 440 = 180 β : 440 - 140 = 300 γ : 140 - 20 = 120$
Check: $180 + 300 + 120 = 600$ , which matches the corrected count rate with no absorber, $620 - 20 = 600$ counts/min. The three parts account for everything.

Answer: The source emits α, β and γ. Count rate due to α: $180$ counts/min; due to β: $300$ counts/min; due to γ: $120$ counts/min.

Example 2. A narrow beam containing α-particles, β-particles and γ-radiation travels horizontally from left to right, in a vacuum, between two horizontal parallel plates. The upper plate is negative and the lower plate is positive. Describe the path of each emission between the plates.

Show the working

Start with the field. It points from the positive plate to the negative plate, so here it points upwards, from the lower plate to the upper plate.
The force on a positive charge is along the field, so upwards. α-particles are positive: they curve upwards, towards the upper (negative) plate.
The force on a negative charge is opposite to the field, so downwards. β-particles curve downwards, towards the lower (positive) plate.
Compare the amounts. A β-particle's mass is far smaller than an α-particle's, so its acceleration is far larger and its path bends much more sharply.
γ-radiation is uncharged, so no force acts on it and it goes straight on.

Answer: α-particles curve gently upwards towards the negative plate; β-particles curve downwards, much more sharply, towards the positive plate; γ-radiation passes straight through undeflected.

Example 3. The same beam, still moving from left to right, now enters a magnetic field directed out of the page. Predict the direction in which the α-particles and the β-particles are deflected as they enter the field, and how their paths differ.

Show the working

Use Fleming's left-hand rule. First finger along the field: pointing out of the page, towards you.
For α, the conventional current is in the direction of travel, so the second finger points right. The thumb then points down the page. α-particles are deflected downwards.
For β, the particles are negative, so the conventional current is opposite to their motion: the second finger points left. The thumb now points up the page. β-particles are deflected upwards.
Opposite charges, opposite deflections, which is a quick check that you have not made a slip.
Both paths are arcs of circles, because the force is always at right angles to the motion. The β arc is much tighter because the β-particle's mass is far smaller. γ is undeflected.

Answer: α-particles are deflected down the page along a large, gentle arc; β-particles are deflected up the page along a much tighter arc; γ-radiation goes straight on.

Example 4. Explain, with reference to electric charge and kinetic energy, why α-particles are more strongly ionising than β-particles.

Show the working

The question names two factors, so plan two parts and keep them separate.
Charge first. Ionising means removing electrons from atoms, and the radiation does this through the electric force on those electrons. α has a charge of +2, twice the size of β's −1, so it exerts a larger force on each electron.
Kinetic energy next. Each ionisation takes energy from the particle's kinetic energy. The α-particle has a large kinetic energy but also a large mass, so it moves slowly and spends longer near each atom.
Finish with the consequence: it ionises many atoms per centimetre and gives away all its kinetic energy in a short distance. A β-particle, light and fast with a smaller charge, ionises far fewer atoms per centimetre.

Answer: α-particles have twice the charge of β-particles, so they exert a larger electric force on the electrons in the atoms they pass and remove electrons more easily. α-particles have a large kinetic energy but a large mass, so they move slowly, spend longer near each atom and transfer their kinetic energy to many atoms over a short distance. β-particles move fast and have a smaller charge, so they ionise fewer atoms per unit length.

Where people go wrong

Mistake: Saying a β-particle is one of the atom's orbiting electrons that has been thrown out.

Instead: A β-particle is an electron emitted from the nucleus, created when a neutron changes into a proton and an electron.

β-radiation is a nuclear emission. The orbiting electrons play no part in it, and the nucleus does not store electrons; the β-particle is made at the moment of emission.

Mistake: Saying α-particles are deflected more than β-particles because they have the bigger charge.

Instead: β-particles are deflected much more, in both electric and magnetic fields.

α has twice the charge but over 7000 times the mass. The mass difference wins, so the β-particle's acceleration is far larger.

Mistake: Using Fleming's left-hand rule with the second finger along the direction the β-particles travel.

Instead: For β-particles, point the second finger opposite to their direction of travel.

The second finger shows conventional current, which is the direction positive charge would flow. Negative particles moving one way are a current in the other direction.

Mistake: Writing that lead stops γ-radiation completely.

Instead: Write that thick lead absorbs most of the γ-radiation, or greatly reduces it.

γ does not cut off sharply the way α does at paper. Each extra thickness of lead lets a smaller fraction through, so 'stops completely' overstates it.

Mistake: Thinking the most strongly ionising emission must also be the most penetrating, because it sounds the 'strongest'.

Instead: The orders are opposite: α ionises most and penetrates least; γ ionises least and penetrates most.

Each ionisation uses up some of the radiation's energy. Radiation that ionises heavily spends its energy within a short distance, so it cannot get far.

Check yourself

What does it mean to say that the emission of radiation from a nucleus is spontaneous?
Answer
It happens by itself: nothing outside the nucleus causes it, and changing conditions such as temperature or pressure, or combining the material chemically, has no effect on it.
A GM tube is placed $3$ cm to one side of a small source. Why does it detect only a small fraction of the radiation the source emits?
Answer
Emission is random in direction, so radiation goes out in all directions. Only the small part that happens to head towards the tube reaches it.
State the nature of an α-particle, a β-particle and γ-radiation.
Answer
α: two protons and two neutrons (a helium nucleus). β: a fast-moving electron emitted from the nucleus. γ: high-frequency electromagnetic radiation.
Put α, β and γ in order of ionising effect, strongest first. Then put them in order of penetrating ability, most penetrating first.
Answer
Ionising: α, β, γ. Penetrating: γ, β, α. The two orders are reversed.
The background count rate is $23$ counts/min. A source gives $812$ counts/min with no absorber, $806$ counts/min with a sheet of paper, and $24$ counts/min with $3$ mm of aluminium. Which emission or emissions does it give out?
Answer
β only. Paper makes no real difference (806 against 812 is random variation), so there is no α. Aluminium brings the count rate down to background (24 against 23), so there is no γ.
A beam of α, β and γ passes between two oppositely charged plates. Which emission is deflected towards the positive plate, and which is not deflected at all?
Answer
β-particles are deflected towards the positive plate. γ-radiation is not deflected.
A beam of β-particles travels up the page through a magnetic field directed into the page. In which direction is the beam deflected?
Answer
To the right. First finger into the page, second finger pointing down the page (conventional current is opposite to the motion of negative particles), and the thumb points right.
Explain why γ-radiation is only weakly ionising.
Answer
It has no charge, so it exerts no electric force on the electrons of the atoms it passes. Most γ-rays pass many atoms without interacting, so few atoms are ionised.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. A teacher has three sealed radioactive sources. One emits only α-particles, one emits only β-particles and one emits only γ-radiation.

(a) State the nature of (i) an α-particle, (ii) a β-particle, (iii) γ-radiation. 3 marks No calculator

Mark scheme

B1 (i) two protons and two neutrons / a helium nucleus
B1 (ii) a (fast-moving) electron (emitted from the nucleus)
B1 (iii) electromagnetic radiation / electromagnetic wave (of high frequency); insufficient: 'a ray' or 'energy' alone

(b) State which of the three emissions is (i) the most strongly ionising, (ii) the most penetrating. 2 marks No calculator

Mark scheme

B1 (i) α-particles
B1 (ii) γ-radiation

Question 2. A student places a source $2$ cm from a GM tube connected to a counter. The background count rate is $25$ counts/min. With different absorbers between the source and the tube she records: no absorber, $1040$ counts/min; a sheet of paper, $1036$ counts/min; $4$ mm of aluminium, $385$ counts/min; $3$ cm of lead, $61$ counts/min.

(a) Deduce which types of emission the source gives out. Use the readings to support each conclusion. 3 marks No calculator

Mark scheme

B1 no α: the paper causes no significant change in count rate (1040 to 1036 is random variation)
B1 β present: the aluminium causes a large fall in count rate
B1 γ present: the count rate with aluminium (385 counts/min) is well above background / the radiation passes through aluminium and is reduced by lead

(b) Calculate the count rate due to the γ-radiation alone. 2 marks

Mark scheme

C1 385 − 25 seen
A1 360 counts/min; unit required (accept counts per minute)

(c) Another student suggests that cooling the source in a freezer would reduce its count rate. Comment on this suggestion. 2 marks No calculator

Mark scheme

B1 the suggestion is wrong / cooling would have no effect on the emission (owtte)
B1 emission is spontaneous / is not affected by temperature or other external conditions

Question 3. A narrow beam containing α-particles, β-particles and γ-radiation travels vertically upwards, in a vacuum, between two vertical parallel plates. The left-hand plate is positive and the right-hand plate is negative.

(a) Describe the path of each of the three emissions between the plates. 3 marks No calculator

Mark scheme

B1 α-particles deflected / curve towards the right-hand (negative) plate
B1 β-particles deflected towards the left-hand (positive) plate / in the opposite direction to α
B1 γ-radiation undeflected / continues in a straight line

(b) Explain why the β-particles are deflected more than the α-particles. 2 marks No calculator

Mark scheme

B1 β-particles have a much smaller mass (than α-particles)
B1 so they have a larger acceleration / are deflected more for the force on them, even though their charge is smaller; accept: β-particles have a much larger charge-to-mass ratio; ORA

(c) The plates are removed and replaced by a magnetic field directed out of the page. Predict the direction in which the β-particles are deflected as they enter the field. 1 mark No calculator

Mark scheme

B1 to the left (towards where the left-hand plate was)

Question 4.

(a) Explain, with reference to electric charge and kinetic energy, why α-particles are more strongly ionising than β-particles. 3 marks No calculator

Mark scheme

B1 α-particles have a larger charge (+2 compared with −1), so exert a larger force on electrons in atoms
B1 α-particles have a large kinetic energy and a large mass, so move slowly / spend longer near each atom; accept: α-particles have more kinetic energy (than β-particles) (so can ionise more atoms)
B1 so they ionise many atoms per unit length / transfer their kinetic energy in a short distance; ORA for β

How this is examined

Deciding which emissions a source gives out from its count rates behind paper, aluminium and lead: a table of count rates with different absorbers, followed by a Deduce of which emissions are present and a short Calculate of the count rate due to one of them One mark per emission, each tied to a reading: 'paper makes no significant change, so no α'; 'aluminium causes a large fall, so β'; 'the count rate behind the aluminium is well above background, so γ'. For the count rate due to γ: reading behind the aluminium minus background, with the unit counts/min.
Which way α, β and γ bend between charged plates or in a magnetic field, and which bends most: a Describe, Sketch or Predict of the paths through charged plates or a magnetic field, with an Explain of why β is deflected more than α Three separate points: α towards the negative plate; β towards the positive plate, opposite to α; γ straight on, undeflected. Then 'β is deflected more because its mass is much smaller'. In a magnetic field, apply Fleming's left-hand rule with the current along the α beam and against the β beam; the charged paths are arcs of circles.
Recalling what each emission is, what stops it, and how strongly it ionises: a State, or a table to complete with rows for nature, charge, what absorbs it and ionising effect α: two protons and two neutrons (helium nucleus), charge +2, stopped by paper, strongly ionising. β: fast-moving electron from the nucleus, charge −1, stopped by a few mm of aluminium. γ: electromagnetic radiation, no charge, greatly reduced by several cm of lead, weakly ionising.
Why α ionises more than β, explained through charge and kinetic energy: a 2- or 3-mark Explain that names both factors Charge: 'α has a larger charge, so a larger force on the electrons in atoms'. Kinetic energy: 'α has a large kinetic energy and a large mass, so it moves slowly, spends longer near each atom and transfers its energy to many atoms in a short distance'; the simpler 'α has more kinetic energy than β' also earns the kinetic-energy point. The same points made in reverse about β are equally valid.
What 'spontaneous' and 'random in direction' mean: a 1- or 2-mark State, or a Comment on a suggestion that heating or cooling a source would change its emission 'Spontaneous: not affected by external conditions such as temperature or pressure.' 'Random in direction: radiation goes out in all directions and the direction of any one emission cannot be predicted.' In a Comment, say the change would have no effect and give that reason.

Words to know

Spontaneous (emission): Happening by itself, not caused or affected by anything outside the nucleus such as temperature or pressure.
Random in direction: Each emission may leave in any direction, and which direction cannot be predicted.
α-particle: Two protons and two neutrons (a helium nucleus) emitted from a nucleus; relative charge +2, relative mass 4.
β-particle: A fast-moving electron emitted from a nucleus; relative charge −1.
γ-radiation: High-frequency electromagnetic radiation emitted from a nucleus; no mass and no charge.
Ionising effect: How strongly radiation removes electrons from the atoms it passes through, turning them into ions.
Penetrating ability: How much material radiation can pass through before it is absorbed.
Deflection: The bending of a beam's path by the force on it from an electric or magnetic field.

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