Physics · 5 Nuclear physics

5.2.4 Half-life

Before you start

Radioactive decay is spontaneous and random, and in alpha or beta decay the nucleus becomes a nucleus of a different element (5.2.3).
The nature of alpha, beta and gamma radiation, their relative ionising effects and their relative penetrating abilities (5.2.2).
Background radiation, count rate in counts/s or counts/minute, and corrected count rate = measured count rate − background count rate (5.2.1).
Reading a value off a graph by going across from one axis to the curve and then down to the other axis.

Syllabus objectives covered (3)

Define the half-life of a particular isotope as the time taken for half the nuclei of that isotope in any sample to decay; recall and use this definition in simple calculations, which might involve information in tables or decay curves (calculations will not include background radiation)
Calculate half-life from data or decay curves from which background radiation has not been subtracted
Explain how the type of radiation emitted and the half-life of an isotope determine which isotope is used for applications including: (a) household fire (smoke) alarms (b) irradiating food to kill bacteria (c) sterilisation of equipment using gamma rays (d) measuring and controlling thicknesses of materials with the choice of radiations used linked to penetration and absorption (e) diagnosis and treatment of cancer using gamma rays

Part 1 of 7

What half-life means

You cannot predict when any one unstable nucleus will decay. Decay is random (5.2.3), so a particular nucleus might decay in the next second or not for a very long time.
A sample contains an enormous number of nuclei, though, and with that many the randomness averages out into a very regular pattern. In equal lengths of time, the same fraction of the nuclei that are still left decays.
Half-life is the time in which that fraction is one half. The definition you must give is: the half-life of a particular isotope is the time taken for half the nuclei of that isotope in any sample to decay.
Nothing on Paper 4 gives you this definition, so learn it word for word. Every phrase in it is doing a job, and the next three steps take them one at a time.
'Half the nuclei'. It is the number of undecayed nuclei of the isotope that halves. It is not the mass of the sample or the size of the sample, so do not write either of those.
'Of that isotope'. Each isotope has its own half-life. Half-lives range from fractions of a second to billions of years, depending on the isotope.
'In any sample'. The half-life does not depend on how much of the isotope you have. A large sample and a small sample of the same isotope have the same half-life; the large one simply has more nuclei to halve.
Now the step that catches people. After one half-life, half the original nuclei are left undecayed. During the next half-life, half of those decay, so after two half-lives a quarter of the original is left, not none.
The count rate falls in the same way. With the source and detector kept in the same positions, the number of decays per second is proportional to the number of undecayed nuclei, so the corrected count rate also halves every half-life. That is why a question can give you nuclei or count rates: you treat them the same way.

Part 2 of 7

Calculations by repeated halving

A simple half-life calculation asks one of three things: what is left after a given time, how long it takes to fall to a given value, or what the half-life is. All three use the same tool, which is counting half-lives.
First find how many half-lives fit into the time.
$number of half-lives = \frac{time}{half-life}$
Then halve once for each half-life, and write the chain out. For $8000$ undecayed nuclei with a half-life of $5$ minutes, after $15$ minutes there are $15 \div 5 = 3$ half-lives, so $8000 \to 4000 \to 2000 \to 1000$ . The chain shows your method, and it is hard to get wrong.
As a fraction of the original, the amount left after $n$ half-lives is one half multiplied by itself $n$ times: $\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{1}{8}$ , $\frac{1}{16}$ and so on.
$fraction left = \frac{1}{2^{n}}$
Read the question for the word that tells you what it wants: left (undecayed) or decayed. After 3 half-lives $\frac{1}{8}$ is left, so $\frac{7}{8}$ has decayed. A correct calculation of the wrong one is still a wrong answer.
To find the half-life itself, work backwards. Count how many halvings take the starting value to the final value, then divide the time by that number. If a corrected count rate falls from $640$ to $80$ counts/minute in $30$ minutes, then $640 \to 320 \to 160 \to 80$ is 3 halvings, so the half-life is $30 \div 3 = 10$ minutes.
Repeated halving only works for a whole number of half-lives. For a time that falls between two half-lives, read the value from a decay curve instead.
For this objective there is no background in the numbers: they are already corrected count rates or numbers of nuclei. When a question gives you a background count rate as well, use the method in the section on background below.

Part 3 of 7

Reading half-life from a table or a decay curve

A decay curve is a graph of the number of undecayed nuclei, or of the corrected count rate, against time. It falls steeply at first, then more and more slowly, getting closer and closer to zero.
It flattens because each half-life removes half of what is left. Half of a large amount is a big drop; half of a small amount is a small drop.
To read the half-life from the curve, choose a starting value on the vertical axis. Go across to the curve and down to the time axis, and read the time. Then halve the value, go across and down again, and read the second time. The half-life is the difference between the two times.
graph diagram — not drawn yet
A smooth decay curve of corrected count rate in counts/minute (vertical axis, 0 to 800) against time in minutes (horizontal axis, 0 to 40), passing through 800 at 0, 400 at 10, 200 at 20, 100 at 30 and 50 at 40, with dashed construction lines from 400 across to the curve and down to 10 minutes, and from 200 across to the curve and down to 20 minutes.
800 to 400 and 400 to 200 each take the same 10 minutes. That equal time for every halving is the half-life.
The half-life does not depend on where you start. On the curve described above, $800$ to $400$ takes $10$ minutes, and so do $400$ to $200$ and $600$ to $300$ .
Use that to check yourself. Read the half-life twice, from two different starting values, and take the mean. If the two readings disagree badly, you have misread the graph.
The trap here is starting somewhere other than $t = 0$ and then quoting the time of the second reading. If the count rate is $600$ counts/minute at $3$ minutes and $300$ counts/minute at $13$ minutes, the half-life is $13 - 3 = 10$ minutes, not $13$ minutes. The half-life is the time between the two readings.
With a table, do the same thing with the numbers. Look for a reading that is half of an earlier reading; the time between them is the half-life. If no pair of readings halves exactly, plot the decay curve and read the half-life from the graph.

Part 4 of 7

When the readings include background

In a real experiment the detector counts background radiation as well as the radiation from the source, and it cannot tell them apart (5.2.1). So every reading is made of two parts.
$measured count rate = corrected count rate + background count rate$
Only the source's part halves every half-life. The background does not come from the sample, so it stays at about the same value however long you wait.
This means that halving a measured reading gives the wrong half-life. The fix is to subtract the background from every reading you use, then find the time for the corrected count rate to halve.
A graph of measured count rate does not fall towards zero. It levels off at the background count rate, because once the source has almost all decayed, the background is all the detector still records. That flat level tells you the background count rate.
On a curve that has already been drawn you cannot subtract from every point, so turn the method round. Work out which measured reading corresponds to half the corrected value, and look for that reading on the curve.
graph diagram — not drawn yet
Measured count rate in counts/minute (vertical axis, 0 to 700) against time in minutes (horizontal axis, 0 to 30), a smooth curve through 680 at 0, 360 at 5, 200 at 10, 120 at 15, 80 at 20, 60 at 25 and 50 at 30, approaching a horizontal dashed line at 40 labelled 'background count rate'; a second, lighter curve below it labelled 'corrected count rate' passes through 640 at 0, 320 at 5, 160 at 10, 80 at 15 and 40 at 20 and approaches zero.
The measured curve levels off at the background, not at zero. Only the gap between the measured curve and the dashed line halves every half-life.
For example, a measured curve starts at $520$ counts/minute and levels off at $20$ counts/minute. The corrected starting value is $520 - 20 = 500$ , half of that is $250$ , and adding the background back gives a target reading of $250 + 20 = 270$ counts/minute. Half of $520$ , which is $260$ , is the wrong target.
To predict a future measured reading, go the other way: correct the reading, halve the corrected value once for each half-life, then add the background back on. Forgetting to add it back is the same mistake as forgetting to subtract it, made at the other end.

Part 5 of 7

Choosing a source: two questions

For every application in this objective, the choice of isotope comes down to two questions. Which type of radiation does the job? And what half-life suits the job?
The type of radiation is decided by penetration and absorption. Recall from 5.2.2: alpha particles are stopped by a sheet of paper or a few centimetres of air, beta particles are stopped by a few millimetres of aluminium, and gamma rays are only reduced by thick lead or concrete.
Ionising effect runs the other way. Alpha is the most strongly ionising and gamma the least, so radiation that is absorbed inside the body does more damage the more strongly it ionises.
So ask what the radiation must pass through to do its job, and what must absorb it. The right type is the one that gets through what it has to and is absorbed where it should be.
The half-life is decided by how long the source has to keep working. A source inside a device or machine that is used for years needs a long half-life, so that its rate of emission stays nearly constant and it does not need replacing often.
A source put inside a person is the opposite case. It needs a short half-life, so that its rate of emission falls quickly once it has done its job.

Part 6 of 7

Alpha and beta at work: smoke alarms and thickness gauges

Smoke alarms. A household smoke alarm contains a small alpha source, americium-241, which has a half-life of about 430 years. The alpha particles ionise the air between two electrodes in a small chamber, and the ions allow a small current to flow across the gap.
When smoke enters the chamber, the smoke particles absorb alpha particles. Less air is ionised, the current falls, and the circuit sounds the alarm.
Alpha is chosen for three reasons. It is strongly ionising, so a tiny source produces enough ions for a current. It is easily absorbed, so smoke stops it and changes the current. And its range in air is only a few centimetres, so the alpha particles do not get out of the alarm to the people in the room.
A long half-life is chosen because the alarm must work for years. With a half-life of hundreds of years, the rate of emission hardly falls during the alarm's life, so the current stays steady and the source does not need replacing.
Thickness gauges. In a factory making paper, the moving sheet passes between a beta source and a detector. A thicker sheet absorbs more beta particles, so the count rate falls; a thinner sheet absorbs fewer, so the count rate rises.
apparatus diagram — not drawn yet
A sheet of paper moving from left to right between a pair of rollers; to the right of the rollers a beta source sits just above the sheet and a detector directly below it, the detector connected to a counter, with an arrow from the counter back to the rollers labelled 'controls roller pressure'.
The detector counts only the beta particles that get through the paper. Fewer counts means thicker paper, and the rollers respond.
The count rate controls the rollers that squeeze the paper. If the count rate falls, the paper is too thick, so the rollers press harder. If the count rate rises, the paper is too thin, so the rollers press less.
Here is the penetration argument for paper, one radiation at a time. Alpha particles would all be absorbed by the paper whatever its thickness, so the detector would record only background and could show no change.
Gamma rays would pass through the paper almost unaffected, so a small change in thickness would make almost no change in the count rate.
Beta particles are partly absorbed by paper, so the count rate changes measurably when the thickness changes. That is the property the gauge needs. The same reasoning picks gamma for thick metal sheets, which would absorb all the beta particles.
The gauge's source needs a long half-life too, for a reason worth saying in full. The count rate must change only because the thickness changes. If the source decayed noticeably during use, the count rate would fall on its own and the system would wrongly read the paper as too thick.

Part 7 of 7

Gamma at work: food, equipment and cancer

Gamma rays are the most penetrating, so they are chosen whenever the radiation must pass right through something: packaging, a whole piece of food, or the human body.
Irradiating food. Food is exposed to gamma rays, which kill bacteria in it so that it keeps for longer. Because gamma rays penetrate, the food can be treated after it has been packed, and the rays reach the inside of the food, not only its surface.
Irradiated food does not become radioactive. It has been exposed to radiation; no radioactive material has been put into it.
Sterilising equipment. Medical equipment such as syringes is sealed in its packaging and then exposed to gamma rays, which kill bacteria and other microorganisms on it. The packaging stays sealed, so the equipment stays sterile until it is opened.
This method needs no heating, so it suits plastic items that would melt or be damaged by heat sterilisation.
Food irradiation and sterilisation both use a gamma source with a long half-life, so that its rate of emission stays nearly constant and it does not need replacing often.
Diagnosing cancer. A small amount of a gamma-emitting tracer, such as technetium-99m (half-life about 6 hours), is injected into or swallowed by the patient. It collects in the organ being examined, and a detector outside the body records the gamma rays coming out to build up an image. The image shows where the tracer has collected, which can reveal a tumour.
Gamma is chosen because it passes out through the body to the detector, and because it is the least ionising, so it does the least damage on the way. Alpha or beta particles from an organ inside the body would be absorbed in the body: they would not reach the detector, and all their ionising effect would be in the patient's cells.
A short half-life is chosen because the tracer stays in the body after the scan. A half-life of a few hours means the rate of emission falls quickly, so the patient receives a small dose. It must not be too short, though, or the tracer would decay before the scan is finished.
Treating cancer. Beams of gamma rays from a source outside the body are aimed at the tumour from several directions. Where the beams cross, at the tumour, the dose is large enough to kill the cancer cells, while the healthy tissue along each beam's path receives a much smaller dose.
Gamma is chosen because it penetrates deep into the body to reach the tumour. The source is outside the body in a machine that is used for years, so it has a long half-life: its output stays steady and it does not need replacing often.
Notice that the half-life points opposite ways in the two medical uses: short for a source inside the body, long for a source in a machine outside it. Decide which situation the question describes before you write your answer.

Worked examples

Example 1. A sample of a radioactive isotope contains $8.0 \times 10^{10}$ undecayed nuclei. The half-life of the isotope is $8.0$ days. Calculate (i) the number of undecayed nuclei left after $24$ days and (ii) the number of nuclei that have decayed in that time.

Show the working

Count the half-lives first, by dividing the time by the half-life.
$\frac{24}{8.0} = 3 half-lives$
Halve three times, writing the chain so the method is visible.
$8.0 \times 10^{10} \to 4.0 \times 10^{10} \to 2.0 \times 10^{10} \to 1.0 \times 10^{10}$
Check with the fraction. After 3 half-lives $\frac{1}{2^{3}} = \frac{1}{8}$ of the nuclei are left, and $\frac{1}{8}$ of $8.0 \times 10^{10}$ is $1.0 \times 10^{10}$ . The two methods agree.
Part (ii) asks for the nuclei that have decayed, not the ones left. Subtract the number left from the original number.
$8.0 \times 10^{10} - 1.0 \times 10^{10} = 7.0 \times 10^{10}$

Answer: (i) $1.0 \times 10^{10}$ undecayed nuclei are left. (ii) $7.0 \times 10^{10}$ nuclei have decayed.

Example 2. The corrected count rate from a radioactive source is recorded every 5 minutes. Time / minutes: 0, 5, 10, 15, 20. Corrected count rate / counts/minute: 960, 680, 480, 340, 240. Determine the half-life of the isotope.

Show the working

These are corrected count rates, so there is no background to remove. Look for a reading that is half of an earlier one.
Half of $960$ is $480$ , which is the reading at $10$ minutes. So the count rate halved between $0$ and $10$ minutes: $10 - 0 = 10$ minutes.
Check with a second pair, because the half-life must be the same from any starting point. Half of $680$ is $340$ : from $5$ minutes to $15$ minutes, which is again $10$ minutes.
A third pair agrees too: $480$ to $240$ runs from $10$ to $20$ minutes. Three pairs giving the same time means the answer is reliable.

Answer: The half-life is $10$ minutes.

Example 3. A student plots the measured count rate from a radioactive source against time, without subtracting background. The curve starts at $680$ counts/minute at $t = 0$ and levels off at $40$ counts/minute. Readings from the curve: $360$ counts/minute at $5.0$ minutes, $200$ counts/minute at $10.0$ minutes and $120$ counts/minute at $15.0$ minutes. Determine the half-life of the isotope.

Show the working

The curve levels off at $40$ counts/minute, not at zero, so the background count rate is $40$ counts/minute. Every reading on the curve includes it.
Correct the starting reading to get the count rate from the source alone.
$680 - 40 = 640 counts/minute$
Halve the corrected value to get $320$ counts/minute. On the measured curve that is the reading $320 + 40 = 360$ counts/minute, because the curve still includes the background.
The curve reads $360$ counts/minute at $5.0$ minutes, so the corrected count rate halved in $5.0$ minutes.
Check with the next pair. The corrected value at $5.0$ minutes is $360 - 40 = 320$ , half of it is $160$ , and $160 + 40 = 200$ counts/minute is reached at $10.0$ minutes. That is again $5.0$ minutes.
See what halving the raw readings would have done. Half of $680$ is $340$ counts/minute, which the curve passes a little after $5.0$ minutes. Half of $200$ is $100$ counts/minute, which the curve does not reach until about $17$ minutes, giving about $7$ minutes instead of $5.0$ . The error grows as the readings get closer to the background.

Answer: The half-life is $5.0$ minutes.

Example 4. Surgical instruments are sealed in plastic bags and then sterilised using a source that emits gamma rays and has a half-life of several years. Explain why this source is suitable.

Show the working

Deal with the type of radiation first. The radiation has to reach the instruments without the bags being opened, so it must be penetrating. Gamma rays are the most penetrating type, so they pass through the sealed bags and the instruments.
Say what the radiation does when it gets there: it kills bacteria and other microorganisms on the instruments, which is what sterilising means.
Link it to the packaging. Because the bags are never opened, the instruments stay sterile until they are used.
Now the half-life. The source is used in the same machine for years, so a half-life of several years means its rate of emission stays nearly constant and the source does not need replacing often.

Answer: Gamma rays are very penetrating, so they pass through the sealed bags and kill the bacteria on the instruments, which stay sterile because the bags stay sealed. The long half-life keeps the rate of emission nearly constant, so the source does not need replacing often.

Where people go wrong

Mistake: Halving the measured count rate when the readings still include background.

Instead: Subtract the background from the readings first, then find the time for the corrected count rate to halve.

Only the count rate from the source halves each half-life; the background stays about the same. Halving the total sets a target that is too low, so it gives a half-life that is too long.

Mistake: Thinking a sample has completely decayed after two half-lives.

Instead: After two half-lives a quarter of the original nuclei is left; after three, an eighth.

Each half-life halves the amount left at the start of that half-life, not the original amount.

Mistake: Defining half-life as 'half the time it takes the sample to decay' or 'the time for the sample's mass to halve'.

Instead: Half-life is the time taken for half the nuclei of that isotope in any sample to decay.

It is the number of undecayed nuclei of the isotope that halves. That is not the same as the mass of the sample, and there is no fixed time in which a sample finishes decaying.

Mistake: Choosing gamma to monitor the thickness of paper because it is the most penetrating.

Instead: Use beta for paper.

The count rate must change when the thickness changes. Gamma passes through paper almost unaffected, so thickness changes barely alter the count rate; beta is partly absorbed, so they do.

Mistake: Saying that irradiated food or sterilised equipment becomes radioactive.

Instead: It does not become radioactive.

It has been exposed to gamma rays, which kill the bacteria; no radioactive material has been put into it.

Check yourself

Define the half-life of an isotope.
Answer
The time taken for half the nuclei of that isotope in any sample to decay.
What fraction of the original undecayed nuclei is left after 4 half-lives, and what fraction has decayed?
Answer
$\frac{1}{2} \to \frac{1}{4} \to \frac{1}{8} \to \frac{1}{16}$ , so $\frac{1}{16}$ is left and $\frac{15}{16}$ has decayed.
The corrected count rate from a source falls from $1200$ counts/minute to $150$ counts/minute in $36$ hours. Calculate the half-life.
Answer
$1200 \to 600 \to 300 \to 150$ is 3 half-lives, so the half-life is $36 \div 3 = 12$ hours.
A decay curve shows a corrected count rate of $600$ counts/minute at $2$ minutes and $300$ counts/minute at $9$ minutes. State the half-life, and say why it is not $9$ minutes.
Answer
$9 - 2 = 7$ minutes. The half-life is the time between the two readings, and the first reading was at $2$ minutes, not at $0$ .
The background count rate is $30$ counts/minute. A source gives a measured count rate of $510$ counts/minute at $t = 0$ , and its half-life is $2.0$ hours. Predict the measured count rate after $4.0$ hours.
Answer
Corrected: $510 - 30 = 480$ . Two half-lives: $480 \to 240 \to 120$ . Add the background back: $120 + 30 = 150$ counts/minute.
A curve of measured count rate starts at $830$ counts/minute and levels off at $30$ counts/minute. Which measured reading should you look for on the curve to find the first half-life?
Answer
Corrected start $= 830 - 30 = 800$ , half of that is $400$ , and $400 + 30 = 430$ counts/minute. Find the time at which the curve reads $430$ counts/minute.
Why are gamma rays, and not alpha particles, used to treat a tumour deep inside the body, and why are the beams aimed from several directions?
Answer
Gamma rays penetrate deep into the body and reach the tumour; alpha particles would be absorbed near the surface of the body. Where the beams cross, the tumour receives a large dose, while the healthy tissue along each path receives a smaller one.
Food can be irradiated with gamma rays after it has been packed. Explain why gamma rays are used, and state whether the food becomes radioactive.
Answer
Gamma rays are very penetrating, so they pass through the packaging and into the food, killing bacteria. The food does not become radioactive.

Exam questions

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

Question 1. A student measures the count rate from a radioactive source every 2 hours. The background count rate in the laboratory is $25$ counts/minute, and the readings below have not been corrected for it. Time / hours: 0, 2, 4, 6, 8. Measured count rate / counts/minute: 425, 308, 225, 166, 125.

(a) Define the half-life of an isotope. 1 mark No calculator

Mark scheme

B1 the time taken for half the nuclei (of that isotope in a sample) to decay; accept atoms for nuclei

(b) Calculate the half-life of the isotope. Show your working. 3 marks

Mark scheme

C1 background subtracted from the readings, e.g. corrected values 400, 200 and 100 counts/minute seen
C1 time for the corrected count rate to halve identified, e.g. 400 at 0 h to 200 at 4 h
A1 4.0 hours or 240 minutes; unit required

(c) Predict the measured count rate at 12 hours. 2 marks

Mark scheme

C1 corrected count rate at 12 hours = 50 counts/minute; ecf from (b)
A1 75 counts/minute; unit required

Question 2. Two devices each contain a radioactive source with a long half-life. A household smoke alarm contains americium-241, which emits alpha particles. A paper mill uses a source that emits beta particles, placed above a moving sheet of paper with a detector below it.

(a) Explain how the alpha particles allow the smoke alarm to detect smoke, and why alpha particles are suitable for this use. 3 marks No calculator

Mark scheme

B1 alpha particles ionise the air inside the alarm, so a (small) current flows
B1 smoke absorbs the alpha particles, so the current falls and the alarm sounds
B1 any one reason alpha is suitable: alpha particles have a short range in air / do not get out of the alarm, so people nearby are not exposed OR alpha particles are strongly ionising, so a small source gives enough ions for a current

(b) Explain why the paper mill uses beta particles rather than alpha particles or gamma rays. 3 marks No calculator

Mark scheme

B1 alpha particles would all be absorbed by the paper, whatever its thickness
B1 gamma rays would pass through (almost) unaffected, so a change in thickness would hardly change the count rate
B1 beta particles are partly absorbed, so the count rate changes as the thickness changes

(c) Explain why both sources need a long half-life. 2 marks No calculator

Mark scheme

B1 the rate of emission (and so the current or count rate) stays almost constant during use
B1 so the source does not need replacing often / so a change in reading is caused by smoke or by thickness, not by decay of the source

Question 3. A hospital uses a tracer that emits gamma rays and has a half-life of $6.0$ hours to examine an organ inside a patient's body. The tracer is injected into the patient, and a detector outside the body records the radiation.

(a) Explain why a gamma emitter with a half-life of $6.0$ hours is suitable for this use. 3 marks No calculator

Mark scheme

B1 gamma rays pass out through the body, so they can be detected outside it OR gamma rays are the least ionising, so they cause least damage to the patient's cells
B1 short half-life, so the rate of emission falls quickly and the patient receives a small dose
B1 half-life long enough for the examination to be completed

(b) Calculate the fraction of the tracer's original nuclei that are still undecayed $24$ hours after the injection. 2 marks

Mark scheme

C1 24 / 6.0 = 4 half-lives
A1 1/16 or 0.0625 or 6.25% or any equivalent

How this is examined

Why one type of radiation suits a named use and the other two do not: a 2- or 3-mark Explain about one application, such as why a thickness gauge for paper uses beta rather than alpha or gamma Naming the radiation and linking each choice to penetration and absorption. For paper: alpha would all be absorbed by the paper; gamma would pass through almost unaffected, so the count rate would hardly change; beta is partly absorbed, so the count rate changes with thickness.
Finding the half-life when the readings still include background: a table or decay curve of measured count rate with the background count rate stated in the question, followed by a 3-mark Calculate or Determine Corrected values shown (each reading minus the background), then the time for the corrected count rate to halve, then the half-life with its unit.
Why the half-life suits the use: a 2-mark Explain following the radiation-type part of an application question Long half-life: the rate of emission stays nearly constant during use, so the source does not need replacing (and for a gauge, a change in count rate is caused by thickness, not by decay). Short half-life for a tracer: the rate of emission falls quickly so the patient's dose is small, but it lasts long enough for the scan.
What is left after a whole number of half-lives, or the half-life from start and end values: a 2- or 3-mark Calculate using numbers of nuclei or corrected count rates, which may be given in a table or read from a decay curve The number of half-lives shown (time divided by half-life, or the count of halvings), then the final value with its unit. Check whether the question asks for the amount left or the amount decayed.
The definition of half-life: a 1-mark Define 'The time taken for half the nuclei (of that isotope in a sample) to decay'. Both 'half the nuclei' and 'to decay' must be there; 'the time for the mass to halve' is not the definition.

Words to know

Half-life: The time taken for half the nuclei of a particular isotope in any sample to decay.
Undecayed nucleus: A nucleus of the original isotope that has not yet decayed.
Decay curve: A graph of the number of undecayed nuclei, or the corrected count rate, against time. It falls to half its value every half-life.
Background count rate: The count rate recorded when no source is present, caused by background radiation.
Corrected count rate: The measured count rate minus the background count rate: the count rate due to the source alone.
Tracer: A small amount of a radioactive isotope put into the body so that the radiation it emits can be detected from outside to show where it has collected.
Irradiation: Exposing something to radiation. Irradiated food or equipment does not become radioactive.
Sterilisation: Killing bacteria and other microorganisms on an object.

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