Activity and its unit

Definition

Activity

The activity of a radioactive source is the number of nuclei that decay each second.

Definition

Becquerel

The becquerel is the unit of activity, equal to one nuclear decay per second.

Definition

Undecayed nuclei

Undecayed nuclei are the nuclei in a sample that have not yet decayed at a given moment.

A radioactive sample contains an enormous number of unstable nuclei, and each one will decay at some point, but they do not all decay together.
Activity counts how fast the sample as a whole is decaying, measured as the number of nuclei that break down each second.
The unit of activity is the becquerel, symbol $Bq\text{Bq}$ , and $Bq1\ \text{Bq}$ means exactly one decay per second.
Because one decay per second is a tiny rate, real sources are quoted in kilobecquerels or megabecquerels, where $Bq1\ \text{kBq} = 1000\ \text{Bq}$ and $Bq1\ \text{MBq} = 1\,000\,000\ \text{Bq}$ .
Activity depends on two things: how many undecayed nuclei are still present, and how likely each of those nuclei is to decay in the next second.
The second of those is fixed for a given isotope and cannot be altered, so heating a source, dissolving it or grinding it up has no effect on its activity.
The first can only fall, because every decay permanently removes one undecayed nucleus from the sample.
Activity is a rate, not an amount, so a source with a high activity is not necessarily one that contains a lot of material; it may simply be decaying quickly.

Why activity falls over time

At the start there is a large stock of undecayed nuclei, so a large number of them happen to decay each second and the activity is high.
Every one of those decays converts an unstable nucleus into a different nucleus, so the stock of undecayed nuclei is smaller a second later.
With fewer nuclei available to decay, fewer of them decay in the next second, so the activity is lower.
That lower activity in turn removes nuclei more slowly, so the fall in activity itself becomes gentler as time goes on.
The result is a curve that starts steep and flattens out, always heading towards zero but never quite reaching it, which is described as exponential decay.
A useful way to state the mechanism is that the activity at any moment is proportional to the number of undecayed nuclei remaining, so as one falls the other falls with it.
The fall is not perfectly smooth from one reading to the next, so a run of measurements has to be repeated and averaged before the trend can be trusted.

Measuring activity in the laboratory

Definition

Count rate

The count rate is the number of decays detected each second by a radiation detector.

A Geiger-Muller tube connected to a counter is the instrument used to follow how a source is decaying.
What the counter records is a count rate, in counts per second, and this is not the same as the activity of the source.
The count rate is always lower than the activity, for three reasons.
1. Radiation is emitted in all directions, so only the fraction aimed at the tube can be detected.
2. Some radiation is absorbed by the air and by the window of the tube before it can be registered.
3. The tube does not respond to every particle that enters it, and it detects alpha radiation very poorly compared with beta and gamma.
The count rate is still a valid measure of how the activity is changing, because the fraction detected stays roughly constant if the detector and the source are not moved.
Every reading also includes background radiation, which is present in the room whether or not the source is there.
Background must therefore be measured with the source removed and subtracted from every reading, giving a corrected count rate.
In symbols, $rate\text{corrected count rate} = \text{measured count rate} - \text{background count rate}$ .

Practical

Investigating how count rate falls with time

Aim: to measure how the count rate from a short-lived radioactive source falls over time, and to show that the fall is exponential.
Apparatus: a sealed protactinium generator bottle, a Geiger-Muller tube with a counter or datalogger, a stand, boss and clamp, a stopclock, a tray to stand the bottle in, disposable gloves and long-handled tongs.
Variables: time is the independent variable, count rate is the dependent variable, and the distance from the source to the tube, the position of the bottle, the counting interval and the tube's operating voltage are all controlled.
Method, background measurement:
- Set up the Geiger-Muller tube in the clamp with no source anywhere near it, and switch the counter on.
- Record the total number of counts over $s300\ \text{s}$ , then divide by $300$ to obtain the background count rate in counts per second.
- Take this reading before the source is brought out, because background must be known before it can be subtracted.
Method, preparing the source:
- Wearing gloves, lift the sealed bottle with tongs and keep it at arm's length; the bottle is never opened.
- Shake the bottle firmly for several seconds so that the short-lived protactinium passes into the upper organic layer, then stand it in the tray and allow the two layers to separate.
- Clamp the window of the Geiger-Muller tube against the upper layer of the bottle, close to it but not touching, and note the separation so it can be kept the same.
Method, taking readings:
- Start the stopclock and the counter at the same moment, and record the number of counts in each successive $s10\ \text{s}$ interval.
- Continue for at least $s200\ \text{s}$ without moving the bottle or the tube, since any change of distance would change the fraction of radiation detected.
- Convert each interval count into a count rate by dividing by the length of the interval in seconds.
- Subtract the background count rate from every value to obtain the corrected count rate.
- Repeat the whole run after the bottle has been shaken again, then average corresponding readings, because single readings scatter.
Results: the corrected count rate falls steeply at first and then more gradually, and equal time intervals each remove the same fraction of the count rate rather than the same number of counts.
Processing: plot corrected count rate on the vertical axis against time on the horizontal axis, draw a smooth curve of best fit rather than joining the points, and describe the shape of the fall in words.
Watch out: forgetting the background subtraction flattens the tail of the curve; moving the tube during the run changes the detected fraction and puts a step in the graph; too short a counting interval gives so few counts that the scatter hides the trend.
Safety: keep the bottle sealed at all times, handle it with gloves and tongs, hold it away from your body, stand it in a tray in case of leakage, return it to the store immediately after use, and wash your hands afterwards.

Example

Correcting a count rate for background

A counter records $1500$ counts in $s300\ \text{s}$ with no source present.
The background count rate is $1500300=5.0\dfrac{1500}{300} = 5.0$ counts per second.
With the source in place, the counter records $360$ counts in $s10\ \text{s}$ .
The measured count rate is $36010=36\dfrac{360}{10} = 36$ counts per second.
The corrected count rate is $36 - 5.0 = 31$ counts per second.
Every later reading in the same experiment must have the same $5.0$ counts per second taken off it.

Example

Converting between activity and decays

A source is labelled as having an activity of $kBq2.4\ \text{kBq}$ .
Converting the unit gives $Bq2.4\ \text{kBq} = 2.4 \times 1000 = 2400\ \text{Bq}$ .
Since $Bq1\ \text{Bq}$ is one decay per second, the source undergoes $2400$ decays every second.
Over one minute the number of decays is $2400 \times 60 = 144\,000$ .
This figure is only a good estimate if the activity has not fallen noticeably during that minute.

Exam technique

Writing about activity and count rate

Use becquerel or $Bq\text{Bq}$ as the unit of activity, and counts per second for a count rate, because the two are measured and named differently.
Explain the fall in activity through the number of undecayed nuclei, since saying only that the source gets weaker does not earn the reasoning mark.
Mention background subtraction whenever you describe or improve a radioactivity measurement, because it is a standard marking point.
Justify repeats by referring to the scatter between readings and the need to average, rather than to accuracy, which is not credited here.
Say that the detector position must be kept fixed, and give the reason that the detected fraction of the emitted radiation would otherwise change.
Read a value from a graph by drawing construction lines on the axes, because a bare number without them can lose the method mark.

Common Mistake

Do not treat the count rate as the activity, because a detector picks up only a small fraction of the radiation emitted.
Do not leave background radiation in your readings, because it is present whether or not the source is there.
Do not say that activity falls because the nuclei get tired or lose energy, since it falls because there are fewer undecayed nuclei left.
Do not claim that cooling, sealing or dissolving a source changes its activity, because nothing done to the material affects the chance of a nucleus decaying.
Do not describe the activity as reaching zero at a definite time, because the curve approaches zero without ever meeting it.

Self review

Define activity and give its unit.
How many decays per second does an activity of $kBq3.5\ \text{kBq}$ represent?
Explain why the activity of a source decreases over time.
Why is a measured count rate always smaller than the activity of the source?
A background count rate of $0.8$ counts per second is measured. A reading with the source gives $24.5$ counts per second. What is the corrected count rate?
Why must the detector stay in the same position throughout a run?

Activity and its unit

Definition

Activity

The activity of a radioactive source is the number of nuclei that decay each second.

Definition

Becquerel

The becquerel is the unit of activity, equal to one nuclear decay per second.

Definition

Undecayed nuclei

Undecayed nuclei are the nuclei in a sample that have not yet decayed at a given moment.

A radioactive sample contains an enormous number of unstable nuclei, and each one will decay at some point, but they do not all decay together.
Activity counts how fast the sample as a whole is decaying, measured as the number of nuclei that break down each second.
The unit of activity is the becquerel, symbol $Bq\text{Bq}$ , and $Bq1\ \text{Bq}$ means exactly one decay per second.
Because one decay per second is a tiny rate, real sources are quoted in kilobecquerels or megabecquerels, where $Bq1\ \text{kBq} = 1000\ \text{Bq}$ and $Bq1\ \text{MBq} = 1\,000\,000\ \text{Bq}$ .
Activity depends on two things: how many undecayed nuclei are still present, and how likely each of those nuclei is to decay in the next second.
The second of those is fixed for a given isotope and cannot be altered, so heating a source, dissolving it or grinding it up has no effect on its activity.
The first can only fall, because every decay permanently removes one undecayed nucleus from the sample.
Activity is a rate, not an amount, so a source with a high activity is not necessarily one that contains a lot of material; it may simply be decaying quickly.

Why activity falls over time

At the start there is a large stock of undecayed nuclei, so a large number of them happen to decay each second and the activity is high.
Every one of those decays converts an unstable nucleus into a different nucleus, so the stock of undecayed nuclei is smaller a second later.
With fewer nuclei available to decay, fewer of them decay in the next second, so the activity is lower.
That lower activity in turn removes nuclei more slowly, so the fall in activity itself becomes gentler as time goes on.
The result is a curve that starts steep and flattens out, always heading towards zero but never quite reaching it, which is described as exponential decay.
A useful way to state the mechanism is that the activity at any moment is proportional to the number of undecayed nuclei remaining, so as one falls the other falls with it.
The fall is not perfectly smooth from one reading to the next, so a run of measurements has to be repeated and averaged before the trend can be trusted.

Measuring activity in the laboratory

Definition

Count rate

The count rate is the number of decays detected each second by a radiation detector.

A Geiger-Muller tube connected to a counter is the instrument used to follow how a source is decaying.
What the counter records is a count rate, in counts per second, and this is not the same as the activity of the source.
The count rate is always lower than the activity, for three reasons.
1. Radiation is emitted in all directions, so only the fraction aimed at the tube can be detected.
2. Some radiation is absorbed by the air and by the window of the tube before it can be registered.
3. The tube does not respond to every particle that enters it, and it detects alpha radiation very poorly compared with beta and gamma.
The count rate is still a valid measure of how the activity is changing, because the fraction detected stays roughly constant if the detector and the source are not moved.
Every reading also includes background radiation, which is present in the room whether or not the source is there.
Background must therefore be measured with the source removed and subtracted from every reading, giving a corrected count rate.
In symbols, $rate\text{corrected count rate} = \text{measured count rate} - \text{background count rate}$ .

Practical

Investigating how count rate falls with time

Aim: to measure how the count rate from a short-lived radioactive source falls over time, and to show that the fall is exponential.
Apparatus: a sealed protactinium generator bottle, a Geiger-Muller tube with a counter or datalogger, a stand, boss and clamp, a stopclock, a tray to stand the bottle in, disposable gloves and long-handled tongs.
Variables: time is the independent variable, count rate is the dependent variable, and the distance from the source to the tube, the position of the bottle, the counting interval and the tube's operating voltage are all controlled.
Method, background measurement:
- Set up the Geiger-Muller tube in the clamp with no source anywhere near it, and switch the counter on.
- Record the total number of counts over $s300\ \text{s}$ , then divide by $300$ to obtain the background count rate in counts per second.
- Take this reading before the source is brought out, because background must be known before it can be subtracted.
Method, preparing the source:
- Wearing gloves, lift the sealed bottle with tongs and keep it at arm's length; the bottle is never opened.
- Shake the bottle firmly for several seconds so that the short-lived protactinium passes into the upper organic layer, then stand it in the tray and allow the two layers to separate.
- Clamp the window of the Geiger-Muller tube against the upper layer of the bottle, close to it but not touching, and note the separation so it can be kept the same.
Method, taking readings:
- Start the stopclock and the counter at the same moment, and record the number of counts in each successive $s10\ \text{s}$ interval.
- Continue for at least $s200\ \text{s}$ without moving the bottle or the tube, since any change of distance would change the fraction of radiation detected.
- Convert each interval count into a count rate by dividing by the length of the interval in seconds.
- Subtract the background count rate from every value to obtain the corrected count rate.
- Repeat the whole run after the bottle has been shaken again, then average corresponding readings, because single readings scatter.
Results: the corrected count rate falls steeply at first and then more gradually, and equal time intervals each remove the same fraction of the count rate rather than the same number of counts.
Processing: plot corrected count rate on the vertical axis against time on the horizontal axis, draw a smooth curve of best fit rather than joining the points, and describe the shape of the fall in words.
Watch out: forgetting the background subtraction flattens the tail of the curve; moving the tube during the run changes the detected fraction and puts a step in the graph; too short a counting interval gives so few counts that the scatter hides the trend.
Safety: keep the bottle sealed at all times, handle it with gloves and tongs, hold it away from your body, stand it in a tray in case of leakage, return it to the store immediately after use, and wash your hands afterwards.

Example

Correcting a count rate for background

A counter records $1500$ counts in $s300\ \text{s}$ with no source present.
The background count rate is $1500300=5.0\dfrac{1500}{300} = 5.0$ counts per second.
With the source in place, the counter records $360$ counts in $s10\ \text{s}$ .
The measured count rate is $36010=36\dfrac{360}{10} = 36$ counts per second.
The corrected count rate is $36 - 5.0 = 31$ counts per second.
Every later reading in the same experiment must have the same $5.0$ counts per second taken off it.

Example

Converting between activity and decays

A source is labelled as having an activity of $kBq2.4\ \text{kBq}$ .
Converting the unit gives $Bq2.4\ \text{kBq} = 2.4 \times 1000 = 2400\ \text{Bq}$ .
Since $Bq1\ \text{Bq}$ is one decay per second, the source undergoes $2400$ decays every second.
Over one minute the number of decays is $2400 \times 60 = 144\,000$ .
This figure is only a good estimate if the activity has not fallen noticeably during that minute.

Exam technique

Writing about activity and count rate

Use becquerel or $Bq\text{Bq}$ as the unit of activity, and counts per second for a count rate, because the two are measured and named differently.
Explain the fall in activity through the number of undecayed nuclei, since saying only that the source gets weaker does not earn the reasoning mark.
Mention background subtraction whenever you describe or improve a radioactivity measurement, because it is a standard marking point.
Justify repeats by referring to the scatter between readings and the need to average, rather than to accuracy, which is not credited here.
Say that the detector position must be kept fixed, and give the reason that the detected fraction of the emitted radiation would otherwise change.
Read a value from a graph by drawing construction lines on the axes, because a bare number without them can lose the method mark.

Common Mistake

Do not treat the count rate as the activity, because a detector picks up only a small fraction of the radiation emitted.
Do not leave background radiation in your readings, because it is present whether or not the source is there.
Do not say that activity falls because the nuclei get tired or lose energy, since it falls because there are fewer undecayed nuclei left.
Do not claim that cooling, sealing or dissolving a source changes its activity, because nothing done to the material affects the chance of a nucleus decaying.
Do not describe the activity as reaching zero at a definite time, because the curve approaches zero without ever meeting it.

Self review

Define activity and give its unit.
How many decays per second does an activity of $kBq3.5\ \text{kBq}$ represent?
Explain why the activity of a source decreases over time.
Why is a measured count rate always smaller than the activity of the source?
A background count rate of $0.8$ counts per second is measured. A reading with the source gives $24.5$ counts per second. What is the corrected count rate?
Why must the detector stay in the same position throughout a run?

6.4.1 Activity and its decrease over time

Activity and its unit

Why activity falls over time

Measuring activity in the laboratory

Investigating how count rate falls with time

Correcting a count rate for background

Converting between activity and decays

Writing about activity and count rate

Review 6.4.1 Activity and its decrease over time by teaching Genie

6.4.1 Activity and its decrease over time

Activity and its unit

Why activity falls over time

Measuring activity in the laboratory

Investigating how count rate falls with time

Correcting a count rate for background

Converting between activity and decays

Writing about activity and count rate

Review 6.4.1 Activity and its decrease over time by teaching Genie

6.4.1 Activity and its decrease over time

Activity and its unit

Why activity falls over time

Measuring activity in the laboratory

Investigating how count rate falls with time

Correcting a count rate for background

Converting between activity and decays

Writing about activity and count rate

Review 6.4.1 Activity and its decrease over time by teaching Genie

6.4.1 Activity and its decrease over time Revision Guide

6.4.1 Activity and its decrease over time

Activity and its unit

Why activity falls over time

Measuring activity in the laboratory

Investigating how count rate falls with time

Correcting a count rate for background

Converting between activity and decays

Writing about activity and count rate

Review 6.4.1 Activity and its decrease over time by teaching Genie

6.4.1 Activity and its decrease over time Revision Guide