GCSE Physics revision

Different half-lives of radioactive isotopes

Hazards and uses of radioactive emissions and of background radiation

AQA 4.4.3.2

Your specification

AQA student objectives

Learning pathway

All · Most · Some

ALL 🎯

Explain why the hazards associated with Radioactive isotopes have a very wide range of half-life values.

MOST 🎯🎯

Apply the scientific explanation of different half-lives of radioactive isotopes to a relevant example.

SOME 🎯🎯🎯

Analyse a new situation involving different half-lives of radioactive isotopes and explain the scientific reasoning.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

The Random Nature of Radioactive Decay

Radioactive decay is a random process, meaning it is impossible to predict which specific nucleus will decay next.
Nothing can be done to speed up or slow down the rate of radioactive decay — heating, cooling, or any other physical change has no effect.
Although individual decays are unpredictable, we can still measure the overall radioactivity of a sample, for example in counts per second using a Geiger counter.

1. The Random Nature of Radioactive DecayAQA

Notes

Radioactive decay is a random process, meaning it is impossible to predict which specific nucleus will decay next.
Nothing can be done to speed up or slow down the rate of radioactive decay — heating, cooling, or any other physical change has no effect.
Although individual decays are unpredictable, we can still measure the overall radioactivity of a sample, for example in counts per second using a Geiger counter.

Defining Half-Life

The half-life is the mean time it takes for the count rate or activity from a sample containing a radioactive isotope to fall to half of its initial level.
A simpler way to think about it: half-life is the time taken for the radioactivity of a sample to drop to half its starting value.
Different radioactive isotopes have different half-lives, which can range from fractions of a second to billions of years.

2. Defining Half-LifeAQA

Notes

The half-life is the mean time it takes for the count rate or activity from a sample containing a radioactive isotope to fall to half of its initial level.
A simpler way to think about it: half-life is the time taken for the radioactivity of a sample to drop to half its starting value.
Different radioactive isotopes have different half-lives, which can range from fractions of a second to billions of years.

Drawing a Half-Life Decay Curve

To draw a decay curve, you only need two pieces of information: the half-life and the starting count rate (or activity).
At each successive half-life interval, the count rate halves again — for example, 84 42 21 10.5 counts per minute.
The resulting graph is always a smooth downward curve (exponential decay), becoming less steep over time but never reaching zero.
The steepness of the curve depends on the half-life value, but the shape is always the same characteristic downward curve.

3. Drawing a Half-Life Decay CurveAQA

Notes

To draw a decay curve, you only need two pieces of information: the half-life and the starting count rate (or activity).
At each successive half-life interval, the count rate halves again — for example, 84 42 21 10.5 counts per minute.
The resulting graph is always a smooth downward curve (exponential decay), becoming less steep over time but never reaching zero.
The steepness of the curve depends on the half-life value, but the shape is always the same characteristic downward curve.

Reading the Half-Life from a Decay Curve

To find the half-life from a graph, identify the starting count rate, halve it, draw a horizontal line to the curve, then drop a vertical line to the time axis.
The time interval read from the graph represents one half-life of the radioactive isotope.
You can confirm the half-life by repeating this process from the halved value (e.g.
80 40 20), checking that each interval is the same.
If the intervals are not exactly equal due to graph drawing, calculate the mean of the values to find the mean half-life.

4. Reading the Half-Life from a Decay CurveAQA

Notes

To find the half-life from a graph, identify the starting count rate, halve it, draw a horizontal line to the curve, then drop a vertical line to the time axis.
The time interval read from the graph represents one half-life of the radioactive isotope.
You can confirm the half-life by repeating this process from the halved value (e.g.
80 40 20), checking that each interval is the same.
If the intervals are not exactly equal due to graph drawing, calculate the mean of the values to find the mean half-life.

Calculating Time Elapsed from Half-Lives

If you know the half-life and the number of half-lives that have passed, you can calculate total time elapsed using: Total time = number of half-lives × text{half-life duration}.
For example, if the half-life is 20 days and 5 half-lives have passed, the total time elapsed is 5 × 20 = 100 days.

5. Calculating Time Elapsed from Half-LivesAQA

Notes

If you know the half-life and the number of half-lives that have passed, you can calculate total time elapsed using: Total time = number of half-lives × text{half-life duration}.
For example, if the half-life is 20 days and 5 half-lives have passed, the total time elapsed is 5 × 20 = 100 days.

Calculating Remaining Atoms After Multiple Half-Lives

One method uses the equation: Remaining atoms = N_0 / 2^n, where N_0 is the starting number of atoms and n is the number of half-lives elapsed.
For example, starting with 300 million atoms after 5 half-lives: frac{300{,}000{,}000}{2^5} = 9{,}375{,}000 atoms remain.
A more intuitive method is to simply halve the starting number repeatedly, once for each half-life that has passed, giving the same result without needing to memorise a formula.

6. Calculating Remaining Atoms After Multiple Half-LivesAQA

Notes

One method uses the equation: Remaining atoms = N_0 / 2^n, where N_0 is the starting number of atoms and n is the number of half-lives elapsed.
For example, starting with 300 million atoms after 5 half-lives: frac{300{,}000{,}000}{2^5} = 9{,}375{,}000 atoms remain.
A more intuitive method is to simply halve the starting number repeatedly, once for each half-life that has passed, giving the same result without needing to memorise a formula.

Working Out the Number of Half-Lives from Percentages

If a sample has decayed to a known percentage of its original activity, you can count how many times it must have halved to reach that value.
For example, starting at 100% and reaching 12.5% requires three halvings: 100% rightarrow 50% rightarrow 25% rightarrow 12.5%, so three half-lives have passed.
Once you know the number of half-lives, multiply by the duration of one half-life to find the total time elapsed.

7. Working Out the Number of Half-Lives from PercentagesAQA

Notes

If a sample has decayed to a known percentage of its original activity, you can count how many times it must have halved to reach that value.
For example, starting at 100% and reaching 12.5% requires three halvings: 100% rightarrow 50% rightarrow 25% rightarrow 12.5%, so three half-lives have passed.
Once you know the number of half-lives, multiply by the duration of one half-life to find the total time elapsed.

Carbon Dating: A Real-World Application

Radioactive carbon (carbon-14) is present in all living organisms, but once an organism dies, the carbon-14 decays and is not replaced.
By comparing the percentage of radioactive carbon remaining in an ancient sample to that in a living organism today, archaeologists can calculate how many half-lives have passed.
The half-life of carbon-14 is approximately 5,400 years, so if a sample contains 12.5% of the original carbon-14, three half-lives have passed, giving an age of 3 × 5{,}400 = 16{,}200 years.

8. Carbon Dating: A Real-World ApplicationAQA

Notes

Radioactive carbon (carbon-14) is present in all living organisms, but once an organism dies, the carbon-14 decays and is not replaced.
By comparing the percentage of radioactive carbon remaining in an ancient sample to that in a living organism today, archaeologists can calculate how many half-lives have passed.
The half-life of carbon-14 is approximately 5,400 years, so if a sample contains 12.5% of the original carbon-14, three half-lives have passed, giving an age of 3 × 5{,}400 = 16{,}200 years.

Key Terms and Units to Remember

Activity or count rate is measured in counts per second or counts per minute, and is detected using a Geiger counter.
A radioactive isotope is a version of an element with an unstable nucleus that undergoes radioactive decay by emitting alpha, beta, or gamma radiation (or neutrons).
Half-life is always a mean (average) time, reflecting the statistical nature of the large number of atoms involved in any real sample.

9. Key Terms and Units to RememberAQA

Notes

Activity or count rate is measured in counts per second or counts per minute, and is detected using a Geiger counter.
A radioactive isotope is a version of an element with an unstable nucleus that undergoes radioactive decay by emitting alpha, beta, or gamma radiation (or neutrons).
Half-life is always a mean (average) time, reflecting the statistical nature of the large number of atoms involved in any real sample.