Physics
Cambridge IGCSE
Cambridge IGCSE
TOPIC 5: NUCLEAR PHYSICS
In this section we will be looking at how quickly radioactive substances decay. To do this we need to be able to measure ionising radiation. Early researchers in nuclear physics noticed that photographic paper changed colour when exposed to radioactive substances. This change helped them investigate the basic properties of radiation. However, it was the invention of the Geiger-Müller detector and counter ('Geiger counter') that first gave us accurate measurements. (See section 5.2a).
A Geiger counter can measure individual alpha, beta and gamma particles/rays that enter the tube. The standard method is to count how many events there are over a period of time, typically one second. This is the 'count rate' recorded. The count rate will depend on the number of nuclear disintegrations per second, called the total activity of the radioactive substance.
The activity is usually given in units of counts per second (counts/s) or counts per minute (counts/min).
Note: There are some other units used in the field of radioactivity such as becquerels, curies and sieverts, but these are not required for this course.
Radioactivity is a completely random process. You cannot predict exactly when one nucleus will emit a particle, only give a likelihood of it happening over a certain time. The best way of picturing this process is with dice. Dice are like nuclei. You can give the likelihood of an event happening, but not an exact time at which it will happen. In this simple simulation, we will use a throw of '6' to say that a nucleus has emitted a particle and decayed:
Here is a graph to show how many dice will typically remain after each roll. As you can see from figure 2, it produces a curved shape.
Figure 2: Decay curve for the dice simulation
How long do you think it will take for all of the 'nuclei' to decay? The answer is that it will be a long time! It may take ages for the last of the dice to roll a 6 - we cannot tell. However, the shape of the graph will always look similar, and it is this shape that scientists use to describe the speed of an isotope's decay.
Instead of measuring the time until the very last decay, we can find the time taken for half of the nuclei to decay. This is called the half-life of the isotope. For example, if the half-life is 5 minutes, it means that half of the nuclei will decay in five minutes. It also means that from those that remain, half will decay in another 5 minutes, leaving only one quarter of the original number.
Figure 3: Half-life graph
As the nuclei decay, they emit particles. The fewer radioactive nuclei that remain, the lower the number of particles emitted. Instead of trying to count the number of nuclei remaining we can simply measure the activity of the isotope (as shown in figure 3), and measure how long the activity takes to fall to half the original value.
The half-life of a substance is defined as the time it takes for...
Some exam questions will ask you to plot graphs of activity against time, and then find the half-life from the graph. Use construction lines (as shown in green, figure 3) to find the time when the activity drops to half the original value. This shows that you understand the concept, even if you get the answer wrong!
Different isotopes have hugely different half-life values, from trillionths of a second to billions of years. Here are a few common isotopes used in industry and medicine:
| Isotope (application) | Half-life |
|---|---|
| Carbon-14 (carbon dating) | 5700 years |
| technetium-99m (medical tracers) | 6 hours |
| Uranium-238 (age of rocks) | 4.5 billion years |
| Cobalt-60 (radiotherapy) | 5.3 years |
Table 2. Half-life values for isotopes used in medicine and industry
(For comparison only. You are not expected to know these!)
There is no standard formula to use at GCSE level for this topic, but there is a simple process for working out how much of an isotope remains. Remember that we can either:
Let us have a look at a common example:
"Carbon-14 has a half-life of 5700 years. A sample of wood only contains 0.2 milligrams (0.2 mg) of carbon-14 from an original 1.6 mg. What ratio of carbon-14 is left compared to the original? How old is the sample of wood?"
To solve this, we take the original 1.6 mg of carbon-14 and keep halving the mass. How many times do we need to do this before it reaches 0.2 mg?
A great way to show your working is in a table like this:
| number of half-lives | 0 | 1 | 2 | 3 | 4 |
| Time (yrs) | 0 | 5 700 | 11 400 | 17 100 | 22 800 |
| Ratio (remaining:original) | 1:1 | 1:2 | 1:4 | 1:8 | 1:16 |
| Mass remaining (mg) | 1.6 | 0.8 | 0.4 | 0.2 | 0.1 |
Table 1: Calculations using half-life values.
As you can see from the table, after 3 half-lives, the mass has fallen to 0.2 mg. Therefore the age of the sample is 17100 yrs, and The ratio remaining is 1:8.
Questions:
1. Radioactive radon gas can be found in caves in high concentrations. The isotope has a half-life of 3.8 days.
a) The half-life of a substance is defined as the time it takes for...
b) After 3.8 days, the mass will have halved.
After 7.6 days (a further 3.8 days), it will have halved again, down to ¼ of the original value.
The ratio is therefore 1:4 (written as 'isotope remaining:original mass')
.
2. An isotope used in engineering has a half life of approximately 10 years.
If the dangerous isotope is buried for 30 years, what will be the net decline in activity, expressed as a ratio, of the isotope remaining after this period?
For this we will use a table of results to show our working out, halving the activity each half-life:
| number of half-lives | 0 | 1 | 2 | 3 |
| Time (yrs) | 0 | 10 | 20 | 30 |
| Ratio (remaining:original) | 1:1 | 1:2 | 1:4 | 1:8 |
from this table we can see that after 30 years, the ratio remaining is 1:8 compared to the original isotope.
This also means that the activity of the sample compared to the original will be in the ratio 1:8 (or 1/8th the original value).
3. A medical sample of technetium-99m has an activity of 20 000 Bq. It has a half-life of 6.0 hours. What will the activity of the sample be after 24 hours?
Using a table again gives these results:
| number of half-lives | 0 | 1 | 2 | 3 | 4 |
| Time (hours) | 0 | 6 | 12 | 18 | 24 |
| Ratio (remaining:original) | 1:1 | 1:2 | 1:4 | 1:8 | 1:16 |
| Activity (Bq) | 20 000 | 10 000 | 5 000 | 2 500 | 1 250 |
From the table we can see that after 24 hrs, the activity is 1250 Bq.
Some questions will include readings for the background count, and this means taking this into consideration before calculating half-life data. The total reading shown in the question will not all be from the isotope, as some will be from the surroundings. For example, if the background count in an experiment is 20 counts/s, then all the data has to have a reading of 20 counts/s subtracted.
Here is a question for you to try:
Questions:
4. In an experiment, a radioactive isotope of half-life 2 hours has a count rate of 100 counts/s at the start of a timed interval. The background count in the lab was measured to be 20 counts/s.
What will be the measured reading after 4 hours?
First, we have to subtract the background count from the data shown.
This means the initial radiation from the isotope is 100-20 = 80 counts/s
However this is a trick question - this is not the final answer!
The reading recorded will include the background count, so we need to add back in the original 20 counts/s!
This makes the final count = 40 counts/s , answer A
Now test your understanding using these quick, 10 minute questions on this topic from Grade Gorilla:
