The Radiation Lab

The half of the question nobody asks

Ask which radiation is used in a smoke detector and most people can tell you. Ask why the source in it lasts for the life of the building and you will usually get a blank look, because the second question is never asked. Choosing a radioactive source for a job is a decision about two things at once. The type decides what the radiation can do: how far it gets, what stops it, what it can pass through. The half-life decides how long it goes on doing it, and that turns out to matter just as much. A source injected for a medical scan has to stop emitting soon after the pictures are taken. A source sealed inside a smoke alarm has to be working just as well in twenty years. ⭐ And the same property has two faces. What makes a source last is exactly what makes waste a problem for generations. It is one number, doing something useful in one place and something awkward in another. So carry one question through: what does this job need the radiation to do, and for how long? What alpha, beta and gamma actually are, and what stops each of them, is the other module on this topic.

Five measurements, used precisely

Three of these are things you measure and two are things that get in the way of measuring them. Mixing up the first two costs marks constantly.

Measure a half-life properly

A class is finding the half-life of a source with a detector and a stopwatch. Put the method into the order it has to be done.

• With no source anywhere near, record the count rate for a while to find the background level
• Bring the source in and record the count rate at regular intervals
• Subtract the background level from every single reading taken
• Pick a corrected reading and note the time at which it was taken
• Find the later time at which the corrected reading has fallen to half of that value
• Repeat starting from a different reading, and check that the interval comes out the same

Random, and yet dependable

Radioactive decay is completely random: nobody can say when any particular nucleus will decay, or which one will go next. Yet half-life is used to predict a source activity years ahead, and the predictions work. How can both of those be true?

• A half-life is a statement about an enormous number of nuclei at once. Each individual event is unpredictable, but the average behaviour of that many of them is extremely steady
• Decay is only random for the first few half-lives, and settles into a regular pattern after that
• The randomness cancels out, because exactly half of the nuclei decay and half do not
• Half-life is only a rough estimate, and the predictions are not really reliable

Short against long, and what each costs

Neither of these is better. They suit different jobs, and almost every question in this part of the topic is really asking which of these two columns the situation belongs in.

Five choices, five reasons

Work out what is left after an hour

A source has an activity of 6400 becquerels and a half-life of 15 minutes. What is its activity one hour later?

Short, long, or neither

For each situation, decide which half-life it calls for. Three lives.

Counting halvings, and writing it down

Every calculation in this part of the topic is the same three moves, and doing them in order stops almost all of the mistakes. One: how many half-lives have passed? Divide the total time by the half-life. Write that number down before you touch the activity. Two: halve the starting activity once for every one of them. Not once in total, once each. Three: give the unit. Activity is in becquerels, and a bare number is an incomplete answer. ⭐ The net decline is what you get if you express the finish against the start as a ratio. After four half-lives the activity is one sixteenth of what it was, which is a net decline of one to sixteen. Notice that the number of halvings is small and the ratio is large, which is why guessing never works here. ⚠️ And one trap. If a question gives you MEASURED readings rather than activities, subtract the background from every one of them first. A half-life taken from uncorrected readings comes out too long, because the background never decays.

Two claims to strike out

Five statements from a set of revision notes. Tap the TWO that are wrong.

• Half-life is the time taken for the activity of a source to fall to half its value
• The background count must be subtracted from measured readings before a half-life is worked out
• After two half-lives the activity of a source has fallen to zero
• A source with a longer half-life always has a higher activity than one with a shorter half-life
• Activity is measured in becquerels, where one becquerel is one decay per second

The party that empties out

A party fills a hall. Nobody leaves on a schedule, and if you pick out any one guest you have no idea whether they will go in ten minutes or stay until the lights come up. And yet the manager knows almost exactly how many people will still be there at midnight, and staffs the bar accordingly. The reason is that roughly a fixed fraction of whoever is left goes home every half hour. Not a fixed number of people: a fraction. So the crowd thins quickly while it is large and slowly once it is small, and the time it takes to fall to half is much the same whether it started at two hundred or at fifty. That is what makes it a useful number: it does not depend on the size. ⚠️ And one thing to watch. If you count heads by looking through the window, you will also count people walking past outside who were never at the party at all. Count those first, with the hall empty, and take them off every later figure, or every number you write down will be too big and the party will look as though it is emptying more slowly than it is.

Put the proper words back

The number of nuclei decaying each second is called the _____ of a source, and it is measured in _____. The time taken for that to fall to half its value is the _____, and it is the same however much of the source you begin with. Before any measurement is used, the _____ count from natural sources has to be recorded and subtracted, or every reading will be too high. Each time one half-life passes, the activity _____. A substance given to somebody so that a scan can be taken is called a _____, and it is chosen to have a short half-life so that it stops emitting soon afterwards.

Choosing a source for a scan

A hospital needs a substance to give to somebody so that a scan can be taken. Select every property that makes a source suitable for that particular job.

• A half-life of a few hours, so that it stops emitting soon after the images are taken
• Radiation penetrating enough to get out of the body and reach a detector
• A half-life not so short that the source decays before it arrives at the hospital
• A half-life of many years, so that one batch lasts a long time
• Radiation stopped within a few centimetres of tissue, so that it stays where it was put

Four decisions about one number

A physicist is asked four different questions in one week, and every one of them turns on half-life. Each stage sets out where things stand and hands you the decision.

• A hospital is choosing a substance to give somebody so that a scan can be taken within the hour. Decide what half-life the job calls for.
• A colleague asks why the hospital cannot use something with a half-life of a few seconds, which would surely be safer still. Decide what to tell them.
• A manufacturer is choosing the source for a smoke detector, which will be sealed into the unit and never replaced for the life of the building. Decide what is needed and why.
• A student writes that long half-life sources are the dangerous ones and short half-life sources are the safe ones. Decide what is right and what is too simple.

Build the definition and the sum

Assemble the sentence that defines half-life properly and then uses it.

Explain how a source is chosen

Explain what half-life means, why it can be relied on even though decay is random, and how it is used to choose a source for a particular job. Use two contrasting jobs as your examples.

• Define half-life precisely, and say what stays the same wherever on the decline you measure it
• Explain why a random process can still give a dependable number, using the idea of very large numbers
• Describe one job that needs a short half-life, and say exactly why a long one would fail
• Describe one job that needs a long half-life, and say exactly why a short one would fail
• Finish by explaining why the same property that makes a source useful can make waste a problem for generations