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GCSE Physics · GCSEChapter 11 · Radioactivity, nuclear equations and half-life
GCSE · Chapter 11

Radioactivity, nuclear equations and half-life

By the end of this chapter you will be able to

  • Compare alpha, beta and gamma radiation in a table
  • Complete a nuclear equation for an alpha or beta decay
  • Find the half-life from a graph of count rate against time
  • Calculate the count after a number of half-lives, and correct a count for background
  • Choose a suitable source for a use, and explain how radiation is kept safe

You should already know

  • Nuclide notation and isotopes (Chapter 10)
  • Standard form and powers of ten (KS3 Maths)

Where this leads

  • Nuclear fission and fusion (Chapter 12)
  • Energy resources (Chapter 4)

GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Describe alpha, beta and gamma radiation: their nature, charge, penetration and ionising power, Write nuclear equations for alpha and beta-minus decay, and state the change in mass and atomic number for gamma, Explain that radioactive decay is random and unstable nuclei decay; define activity in becquerels, Define half-life, and find it from a graph and from count data; correct count rates for background radiation, Describe uses and dangers of radiation (medical, tracers, dating) and how risks are reduced.

Exercise P  Do you remember?

1
FWhat is 800 divided by 2? Write the number.
2
FWhat is the mass number of an alpha particle? Write the number.
3
FWhich particle is emitted by an electron decay in the nucleus? Write the word: electron or proton.
4
FWhat is 1200 divided by 4? Write the number.
5
FWhich is the largest: 5 minutes, 50 seconds or 1 hour? Write the word: minutes, seconds or hour.
11.1

Alpha, beta and gamma radiation

GCSE
Describe alpha, beta and gamma radiation: their nature, charge, penetration and ionising power
Video lesson: Alpha, beta and gamma radiationComing soon
Context. A smoke alarm contains a tiny source of radiation. Mrs Patel asks whether it is safe to keep in the hall. The answer depends on the type of radiation the source gives out and how much of it escapes.

Some nuclei are unstable. They give out radiation to become more stable. This is called radioactive decay. There are three main types:

RadiationWhat it isChargePenetrationIonising power
alpha (α)two protons and two neutrons+2stopped by paper or a few cm of airstrong
beta (β-)a fast electron from the nucleus-1stopped by about 3 mm of aluminiummoderate
gamma (γ)electromagnetic waves from the nucleus0needs thick lead or concreteweak
The three types of radiation compared
paperaluminiumleadalphabetagammaalpha stopped by paper; beta by aluminium; gamma only by thick lead
What stops each type of radiation

Key ideas

  • Alpha: +2 charge, stopped by paper, strongly ionising.
  • Beta: -1 charge, stopped by aluminium, moderately ionising.
  • Gamma: no charge, needs thick lead or concrete, weakly ionising.
  • Ionising power: how much a radiation knocks electrons out of atoms.
Worked example 11.1.1
Which type of radiation is stopped by a sheet of paper? Write the name.

Method. Compare the penetration of each type.

  1. Look. Alpha is the least penetrating, stopped by paper or a few centimetres of air.
    least penetrating
  2. Decide. So alpha is the type stopped by paper.
    alpha
  3. Write the answer.
    alpha

Check. ✓

Worked example 11.1.2
Which type of radiation needs thick lead to reduce it? Write the name.

Method. Compare the penetration.

  1. Look. Gamma is the most penetrating type.
    most penetrating
  2. Decide. So gamma needs thick lead or concrete.
    gamma
  3. Write the answer.
    gamma

Check. ✓

Worked example 11.1.3
An alpha particle has a charge of +2. Is a beta particle positive or negative? Write positive or negative.

Method. Recall the beta particle.

  1. Recall. A beta-minus particle is an electron, with charge -1.
    -1
  2. Decide. So it is negative.
    negative
  3. Write the answer.
    negative

Check. ✓

Watch out

Watch out: beta-minus is an electron from the nucleus, not one of the orbiting electrons. It is a fast particle with negative charge.

Exam tip

Exam tip. When asked which radiation is most ionising, pick alpha. When asked which penetrates most, pick gamma.

Exercise 11A  Types of radiation

1
FWhich radiation is a helium nucleus? Write the name.
2
FWhich radiation is a fast electron from the nucleus? Write the name.
3
FWhich radiation has no charge? Write the name.
4
FWhat is the charge of an alpha particle? Write the number with its sign.
5
FWhat is the charge of a beta particle? Write the number with its sign.
6
FWhich type of radiation is stopped by a few millimetres of aluminium? Write the name.
7
FWhich type of radiation is the most ionising? Write the name.
8
FWhich type of radiation is the most penetrating? Write the name.
9
PSWhich two types of radiation are deflected by a magnetic or electric field? Write two names, alpha first.
10
RExplain why alpha is more ionising than gamma, in one sentence. Accept any sentence that says alpha is heavy and highly charged, so it knocks electrons out of atoms more easily.
11
RA pupil says “gamma is the most dangerous outside the body because it is most ionising.” Explain why this is wrong. Accept any answer that says gamma is weakly ionising, but it penetrates the body, so it is dangerous from outside.
12
PSWhich radiation is stopped by a sheet of paper, and which is stopped by a few millimetres of aluminium? Write two names: paper first, then aluminium.
13
FWhich type of radiation is an electromagnetic wave? Write the name.
14
PSA radioactive source gives out alpha, beta and gamma. Which one could be stopped by a thin sheet of paper alone? Write the name.
11.2

Nuclear equations and random decay

GCSE
Write nuclear equations for alpha and beta-minus decay, and state the change in mass and atomic number for gamma, Explain that radioactive decay is random and unstable nuclei decay
Video lesson: Nuclear equations and random decayComing soon
Context. A student is writing the equation for the decay of uranium-238. “How do I balance the numbers?” she asks. The mass number and the atomic number must both balance on each side of the arrow.

A nuclear equation shows what happens in a decay. The mass number (top) and the atomic number (bottom) must balance on each side.

Radioactive decay is random: we cannot say when a particular nucleus will decay, only how many will decay in a large sample in a given time.

DecayChange in mass numberChange in atomic numberParticle emitted
alphagoes down by 4goes down by 2helium nucleus, ^4_2He
beta-minusstays the samegoes up by 1electron, ^0_-1e
gammastays the samestays the sameelectromagnetic wave, no mass or charge
How each decay changes the nucleus

Key ideas

  • Balance the mass numbers on both sides, and the atomic numbers on both sides.
  • Alpha: A - 4 and Z - 2.
  • Beta-minus: A stays the same and Z + 1.
  • Decay is random: we cannot predict the exact nucleus that will decay next.
Worked example 11.2.1
Complete the equation for alpha decay of radon-222: 22286Rn → ? + 42He. Write the mass number and atomic number of the new nucleus, separated by a comma.

Method. Subtract the alpha particle from the parent.

  1. Mass. Mass number = 222 - 4 = 218.
    222 - 4 = 218
  2. Atomic. Atomic number = 86 - 2 = 84.
    86 - 2 = 84
  3. Write the answer.
    218, 84

Check. 218 + 4 = 222 and 84 + 2 = 86. ✓

Worked example 11.2.2
Complete the equation for beta-minus decay of carbon-14: 146C → ? + 0-1e. Write the mass number and atomic number of the new nucleus, separated by a comma.

Method. The mass number stays the same; the atomic number goes up by 1.

  1. Mass. Mass number stays 14.
    14
  2. Atomic. Atomic number = 6 + 1 = 7.
    6 + 1 = 7
  3. Write the answer.
    14, 7

Check. 14 = 14 and 7 - 1 = 6. ✓

Worked example 11.2.3
In a sample of 1000 unstable nuclei, can we say exactly which nucleus will decay next? Write yes or no.

Method. Think about random decay.

  1. Look. Each nucleus decays at a random time.
    random
  2. Decide. So we cannot predict which one will decay next.
    no
  3. Write the answer.
    no

Check. ✓

Watch out

Watch out: in an equation, the sum of the top numbers (mass) and the sum of the bottom numbers (atomic) must be the same on both sides.

Exam tip

Exam tip. Write the parent on the left. Subtract 4 and 2 for alpha; keep the mass and add 1 to the atomic number for beta-minus.

Exercise 11B  Nuclear equations

1
FIn alpha decay, by how much does the mass number go down? Write the number.
2
FIn alpha decay, by how much does the atomic number go down? Write the number.
3
FIn beta-minus decay, does the atomic number go up or down? Write up or down.
4
FIn beta-minus decay, does the mass number stay the same, or change? Write the word.
5
FComplete: 23892U → 23490Th + ? Write the name of the particle.
6
PSComplete: 146C → 147N + ?. Write the particle name.
7
PSComplete: 22286Rn → 21884Po + ?. Write the particle name.
8
PSWrite the mass number of the nucleus formed when 21084Po emits an alpha particle. Write the number.
9
PSWrite the atomic number of the nucleus formed when 21084Po emits an alpha particle. Write the number.
10
RExplain in one sentence why gamma decay does not change the element. Accept any sentence that says the number of protons (atomic number) does not change.
11
RA pupil says “we can predict which nucleus will decay next, if we know the source is unstable.” Is the pupil right? Write yes or no.
12
RExplain, in one sentence, what the word random means for radioactive decay. Accept any sentence that says the decay of one nucleus cannot be predicted, but for many nuclei a pattern is seen.
11.3

Activity, count rate and background radiation

GCSE
Explain that radioactive decay is random and unstable nuclei decay; define activity in becquerels, Correct count rates for background radiation
Video lesson: Activity, count rate and background radiationComing soon
Context. A Geiger counter clicks as it detects radiation. The class measures the count rate near a sealed low-activity source, and then without it. The difference is what the source gives out, but the counter also detects background radiation all the time.

The activity of a source is the number of decays each second, measured in becquerels (Bq). A count rate is the number of counts per second or per minute recorded by a detector. The background radiation comes from natural and man-made sources, and it is always present. To find the count rate due to the source alone, subtract the background count rate:

corrected count rate = measured count rate - background count rate

Source of background radiationExample
radon gas in the ground and buildingsthe largest source for most people in the UK
cosmic rays from spacemore at high altitude
rocks and soilsome rocks contain more radioactive material
medicalX-rays and scans
food and drinksmall amounts in what we eat and drink
Sources of background radiation

Key ideas

  • Activity is measured in becquerels: 1 Bq = 1 decay per second.
  • Count rate is measured by a detector, often counts per minute.
  • Background radiation is always present and must be subtracted.
  • Corrected count rate = measured - background.
Worked example 11.3.1
A detector records 120 counts per minute near a source. The background count rate is 20 counts per minute. What is the corrected count rate? Write the number.

Method. Subtract the background from the measured count.

  1. Read. Measured = 120 counts per minute, background = 20 counts per minute.
    120, 20
  2. Subtract. Corrected = 120 - 20 = 100 counts per minute.
    120 - 20 = 100
  3. Write the answer.
    100

Check. 100 + 20 = 120. ✓

Worked example 11.3.2
A source has an activity of 500 Bq. How many decays happen each second? Write the number.

Method. One becquerel is one decay each second.

  1. Convert. Activity = 500 Bq = 500 decays per second.
    500 per second
  2. Read. An activity of 500 Bq means 500 decays each second.
    500 Bq
  3. Decide. So 500 decays per second.
    500
  4. Write the answer.
    500

Check. ✓

Worked example 11.3.3
Name a source of background radiation that comes from the ground and from buildings. Write the word.

Method. Recall the main natural source.

  1. Look. Some natural gases come up through the ground.
    ground
  2. Recall. Radon gas comes from the ground and can build up in buildings.
    radon
  3. Write the answer.
    radon

Check. ✓

Watch out

Watch out: the count rate is usually given per minute, but the activity is in becquerels, which are per second. Convert before you compare.

Exam tip

Practical safety. Only the teacher handles sealed low-activity sources. Pupils keep their distance, and keep the source in its holder. Wash hands after lessons.

Exercise 11C  Activity, count rate and background

1
FWhat is the unit of activity? Write the unit.
2
FA source has an activity of 300 Bq. How many decays happen in 1 second? Write the number.
3
FA detector records 90 counts per minute from a source. The background is 15 counts per minute. Find the corrected count rate. Write the number.
4
FA detector records 200 counts in 1 minute. The background count is 50 counts in 1 minute. What is the count from the source? Write the number.
5
FName a natural source of background radiation that comes from space. Write the words.
6
FName a medical source of background radiation. Write the word.
7
RWhy must the background count be subtracted? Write one reason in one sentence. Accept any sentence that says background radiation is always present, and would add to the count from the source.
8
PSA source gives a count of 480 counts per minute. The background is 60 counts per minute. Calculate the corrected count rate in counts per second. Write the number.
9
PSA source has an activity of 2 kBq (2000 Bq). Calculate the number of decays in 5 minutes. Write the number.
10
PSIn the count-rate data, the measured count is 40 counts per minute with the source and 40 without it. What is the source count? Write the number.
11
RExplain why a count rate measured without any source is not zero, in one sentence. Accept any sentence that says there is background radiation from natural sources all the time.
11.4

Half-life

GCSE
Define half-life, and find it from a graph and from count data
Video lesson: Half-lifeComing soon
Context. A hospital has a radioactive tracer that is used for a short time, and then stored. The staff need to know how long it stays useful. They use the half-life: the time for the activity to halve.

The half-life of a radioactive isotope is the time taken for half the nuclei in a sample to decay. It is also the time for the count rate or activity to halve. Each half-life, the count falls to half of its previous value. Half-lives can be very short (fractions of a second) or very long (millions of years).

To find the count after several half-lives, halve the starting count once for each half-life: after n half-lives the count is the start count divided by 2n.

Count rate against time (example, half-life 20 min)0200400600800020406080time (min)counts per minute
Count rate falls by half each 20 minutes (example)

Key ideas

  • Half-life: time for the activity or count rate to halve.
  • Count after n half-lives = start count / 2 to the power n.
  • Read the half-life from a graph: find the time for the count to halve.
  • Use the corrected count (background subtracted) before finding the half-life.
Worked example 11.4.1
A sample has a count rate of 800 counts per minute, and a half-life of 20 minutes. What is the count rate after 40 minutes? Write the number.

Method. 40 minutes is 2 half-lives, so halve twice.

  1. Count. 40 / 20 = 2 half-lives.
    2
  2. Halve. 800 / 2 = 400, then 400 / 2 = 200 counts per minute.
    200
  3. Write the answer.
    200

Check. 800 / 2 / 2 = 200. ✓

Worked example 11.4.2
On the graph (400 counts per minute at the start), the count falls to 200 counts per minute at 20 minutes. What is the half-life? Write the number of minutes.

Method. Find the time taken for the count to halve.

  1. Read. The count goes from 400 to 200 between 0 and 20 minutes.
    0 to 20
  2. Decide. So the half-life is 20 minutes.
    20 min
  3. Write the answer.
    20 minutes

Check. The count is 100 at 40 minutes, which is half of 200. ✓

Worked example 11.4.3
A sample has 1200 counts per minute at the start. How many counts per minute after 2 half-lives? Write the number.

Method. Halve twice, or divide by 2 squared.

  1. Halve. After 1 half-life: 600. After 2 half-lives: 300.
    600, 300
  2. Check. 1200 / 22 = 1200 / 4 = 300.
    1200 / 4 = 300
  3. Write the answer.
    300

Check. ✓

Watch out

Watch out: the half-life is a time, not a count. Halving the count once takes one half-life, not one minute.

Exam tip

Exam tip. To find the half-life from a graph, start at a count, go down to half of it, then read the time across. Do not use the background count in the reading.

Exercise 11D  Half-life calculations

1
FA sample has a count of 600 counts per minute. After one half-life the count is? Write the number.
2
FA sample has a count of 80 counts per minute. What is the count after one half-life? Write the number.
3
PSA sample has a count of 400 counts per minute and a half-life of 5 minutes. What is the count after 10 minutes? Write the number.
4
PSA sample has a count of 1600 counts per minute and a half-life of 2 hours. What is the count after 6 hours? Write the number.
5
PSA sample has a count of 800 counts per minute and a half-life of 20 minutes. What is the count after 60 minutes? Write the number.
6
PSA radioactive sample has a half-life of 10 days. Its count is 640 counts per minute at the start. What is the count after 30 days? Write the number.
7
PSA sample has a count of 500 counts per minute. After one half-life it is 250, and after another half-life it is 125. How long is one half-life if the total time is 16 minutes? Write the number of minutes.
8
PSRead from the graph: a sample falls from 400 to 100 counts per minute. How many half-lives have passed? Write the number.
9
PSA corrected count falls from 180 counts per minute to 45 counts per minute. How many half-lives is this? Write the number.
10
PSA sample has a half-life of 3 hours. How long does it take for the count to fall to one-eighth of its starting value? Write the number of hours.
11
RExplain why a half-life of 5 days means that half the sample decays in 5 days, not that all decays in 10 days. Accept any answer that says each half-life halves the remaining sample, so it never reaches zero in a fixed time.
12
RA pupil says “the half-life of a source is 10 minutes, so it will be gone after 20 minutes.” Explain why this is wrong. Accept any answer that says after 20 minutes only a quarter remains, not zero.
11.5

Uses and dangers of radiation

GCSE
Describe uses and dangers of radiation (medical, tracers, dating) and how risks are reduced
Video lesson: Uses and dangers of radiationComing soon
Context. A patient is given a radioactive tracer so that a doctor can see how the blood flows through the heart. The tracer must emit gamma rays that escape the body, and it must have a short half-life so that the dose falls quickly.

Radiation has many uses. Gamma sources are used as tracers in medicine, because the gamma rays escape the body and can be detected. Radiotherapy uses radiation to kill cancer cells. Carbon dating uses carbon-14, which has a half-life of about 5700 years, to date old wood and bones.

Radiation is dangerous because it is ionising: it can damage cells and DNA. The risks are reduced by keeping sources in shielded containers, keeping the time of exposure short, and keeping a large distance from the source. Sources are handled with tongs or in a lead container.

Key ideas

  • Gamma: used as a medical tracer; escapes the body.
  • Radiotherapy: radiation kills cancer cells.
  • Carbon dating: carbon-14 (half-life about 5700 years) dates old material.
  • Risks: time, distance and shielding reduce the dose.
Worked example 11.5.1
Which type of radiation is best for a medical tracer that is detected outside the body? Write the name.

Method. Choose the radiation that escapes the body.

  1. Look. Alpha is stopped by the skin and paper, so it does not escape.
    stopped
  2. Decide. Gamma escapes the body and can be detected.
    gamma
  3. Write the answer.
    gamma

Check. ✓

Worked example 11.5.2
A tracer has a half-life of 6 hours. How many half-lives have passed after 1 day? Write the number.

Method. A day is 24 hours.

  1. Time. 1 day = 24 hours.
    24 h
  2. Count. 24 / 6 = 4 half-lives.
    24 / 6 = 4
  3. Write the answer.
    4

Check. ✓

Worked example 11.5.3
State one way to reduce the risk from a radioactive source. Write one method in one sentence. Accept any method that uses time, distance or shielding.

Method. Think about the three ways to reduce exposure.

  1. Options. Time, distance and shielding all reduce the dose.
    time, distance, shielding
  2. Choose. For example, keep the source in a lead container.
    lead container
  3. Write the answer.
    Accept any method that uses time, distance or shielding.

Check. ✓

Watch out

Watch out: a tracer is useful because its half-life is short and its radiation escapes. A long half-life means the source stays active for a long time.

Exam tip

Exam tip. When choosing a source for a use, check two things: does the radiation escape the body (or the object), and is the half-life suitable for the time needed?

Exercise 11E  Uses and dangers

1
FWhich radiation is used as a medical tracer? Write the name.
2
FWhat is the half-life of carbon-14, used in dating? Write the number of years, about.
3
FWhat is radiation used to kill in radiotherapy? Write the word.
4
FWhy is radiation dangerous to the body? Write one word: ionising or heavy.
5
FName one way to reduce exposure to a radioactive source. Write the word: distance, colour or noise.
6
PSA tracer with a half-life of 2 hours is used for a test lasting 8 hours. How many half-lives pass? Write the number.
7
RWhich is the better tracer for a short test: a source with a half-life of 2 hours or one with 2000 years? Write 2 hours or 2000 years.
8
RExplain why a lead container is used to store a gamma source, in one sentence. Accept any sentence that says lead absorbs gamma radiation, reducing the dose to people nearby.
9
RA pupil says “a radioactive source is safe to hold if it is only for a moment.” Explain whether this is correct. Accept any answer that says short exposure reduces the dose but a source must still be handled only by trained people, with tongs or a container.
10
PSCarbon-14 is used to date old wood. A sample has 800 counts per minute when fresh and 100 counts per minute now. How many half-lives have passed? Write the number.
11
PSCarbon-14 has a half-life of about 5700 years. Using 3 half-lives, estimate the age of a sample. Write the number of years.

Chapter summary

SkillMethod
Types of radiationAlpha +2, stopped by paper; beta -1, stopped by aluminium; gamma no charge, needs lead
Nuclear equationsAlpha: A - 4, Z - 2; beta-minus: A same, Z + 1; balance both numbers
Activity and backgroundActivity in Bq (decays per second); corrected count = measured - background
Half-lifeTime for the count to halve; count after n half-lives = start / 2 to the power n
Uses and dangersGamma tracers, radiotherapy, carbon dating; reduce risk with time, distance and shielding

Can you…?

  • I can compare alpha, beta and gamma radiation
  • I can complete nuclear equations for alpha and beta-minus decay
  • I can correct a count rate for background radiation
  • I can find a half-life from a graph and from count data
  • I can explain how radiation is used and how risks are reduced

Key terms

radioactive decay
the random process by which an unstable nucleus gives out radiation
alpha particle
two protons and two neutrons, given out by some nuclei
beta particle
a fast electron given out by a nucleus when a neutron changes to a proton
gamma radiation
electromagnetic waves given out by a nucleus, with no mass or charge
activity
the number of decays each second, in becquerels (Bq)
half-life
the time for the activity or count rate to halve
background radiation
radiation always present from natural and man-made sources

Exercise 11Z  Check-up

1
Which radiation is a helium nucleus? Write the name.
2
Which radiation is stopped by a few millimetres of aluminium? Write the name.
3
Complete: 22688Ra → 22286Rn + ?. Write the particle name.
4
Complete: 146C → 147N + ?. Write the particle name.
5
A sample has 240 counts per minute. How many counts per minute after 1 half-life? Write the number.
6
A sample has a half-life of 4 hours. How long for 3 half-lives? Write the number of hours.
7
A measured count is 70 counts per minute and the background is 10 counts per minute. What is the corrected count? Write the number.
8
What is the unit of activity? Write the unit.
9
Explain why we cannot predict exactly when one nucleus will decay, in one sentence. Accept any sentence that says radioactive decay is random.
10
Name the type of radiation that is best for a tracer used in a body scan. Write the name.

Total 28 marks. Allow about 28 minutes.

Exercise 11X  Exam-style questions

1
PSComplete the nuclear equation: 23892U → 23490Th + ?. Write the particle name.[1 mark]
2
PSA source has a half-life of 5 minutes and starts at 640 counts per minute. Calculate the count after 15 minutes. Write the number.[2 marks]
3
FA detector records 230 counts per minute near a source. The background is 30 counts per minute. Calculate the corrected count rate. Write the number.[2 marks]
4
RComplete: 146C → 147N + ?. Explain your answer in one sentence. Accept any answer that says it is a beta-minus particle (an electron), because the atomic number goes up by 1 and the mass number stays the same.[2 marks]
5
RDescribe how a student could use a graph of count rate against time to find the half-life of a sample. Accept any answer that starts at a count, finds the time for the count to halve, and reads that time as the half-life.[3 marks]
6
RExplain why background radiation must be taken into account when measuring the count rate of a weak source. Accept any answer that says the detector records background, so the measured count is too high unless the background is subtracted.[3 marks]
7
RA radioactive source is used in a smoke detector. Explain which type of radiation is suitable and why, using penetration and ionising power. Accept any answer that says alpha is used because it is stopped by a short distance of air and is strongly ionising, so the source is contained.[4 marks]
8
PSA sample has a count rate of 960 counts per minute at the start, and a half-life of 3 hours. Calculate the count rate after 9 hours. Give your working. Write the number.[3 marks]
9
RExplain how the half-life of carbon-14 is used to estimate the age of a wooden object. Accept any answer that says the carbon-14 count falls by half every 5700 years, so the number of half-lives gives the age.[4 marks]
10
REvaluate the claim: “a source with a half-life of 2 seconds is safer to store than one with a half-life of 2000 years.” Explain your answer. Accept any answer that says the short half-life source loses its activity quickly, so it is less hazardous over time, though it is more active at first.[4 marks]
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