Every choice of isotope comes down to two properties

1. The type of radiation emitted decides whether it can reach where it is needed, because each type is absorbed by different materials.
2. The half-life decides how long the source stays useful, and how long it stays a hazard once the job is done.
3. The rule for the radiation type is that it must reach the target but no further; radiation that stops too soon is useless, and radiation that sails straight through tells you nothing and irradiates whatever is beyond.
4. The rule for half-life depends on where the source sits.
   1. A source sealed inside a device wants a long half-life, so the reading does not drift and nobody has to replace it.
   2. A source that goes inside a person wants a short half-life, so it decays away quickly once the scan is over and the patient's total dose stays low.
   3. A short half-life must still be long enough for the source to be made, delivered and used before it fades.

The five applications and the reasoning behind each one

1. Household fire (smoke) alarms use an alpha emitter with a long half-life.
   1. A tiny americium-241 source ionises the air in a small chamber, and the ions produced allow a steady current to flow between two electrodes.
   2. Smoke particles entering the chamber absorb the alpha particles, the current falls, and the circuit sounds the alarm.
   3. Alpha is the only sensible choice because it is strongly ionising enough to produce that current and easily absorbed enough that smoke blocks it; beta or gamma would pass through the smoke unchanged.
   4. Being easily absorbed also makes it safe on a ceiling, since the alarm casing and a few centimetres of air stop everything that leaves the chamber.
   5. Its half-life of over $400$ years means the alarm works identically on the day it is thrown away as on the day it was fitted.
2. Irradiating food to kill bacteria uses gamma radiation.
   1. The ionising radiation damages the cells of bacteria and moulds on and inside the food, killing them so the food keeps for longer.
   2. Gamma is needed because it penetrates the packaging and the food itself, so items can be treated after they are sealed and cannot be recontaminated.
   3. The food does not become radioactive, because it only absorbs radiation passing through it and no radioactive material is added to it.
   4. A long half-life keeps the plant's source at a steady strength instead of needing constant replacement.
3. Sterilising equipment also uses gamma radiation.
   1. Syringes, dressings and surgical instruments are sealed in their packaging first and then passed through a beam from a source such as cobalt-60.
   2. Gamma penetrates the sealed packaging, so the contents are sterilised without ever being opened and exposed to air.
   3. This works where steam sterilising cannot, because plastic items would melt or warp in the heat.
4. Measuring and controlling the thickness of materials uses a beta emitter with a long half-life.
   1. In a paper or foil mill, the source sits on one side of the moving sheet and a detector on the other, reading the count rate continuously.
   2. A thicker sheet absorbs more radiation, so the count rate drops, and a thinner sheet lets more through, so it rises.
   3. Beta is chosen because it is partly absorbed by that thickness; alpha would be stopped completely and the reading would never change, while gamma would pass through almost unaffected and be just as unresponsive.
   4. The count rate feeds back to the rollers, which squeeze harder or ease off automatically to hold the thickness constant.
   5. The half-life must be long, otherwise a falling count rate from the decaying source would be mistaken for a thickening sheet.
5. Diagnosis and treatment of cancer use gamma rays, in two different ways.
   1. For diagnosis, a patient is given a gamma-emitting tracer that collects in the organ being studied, and a detector outside the body builds up an image of where it goes.
   2. Gamma is essential there because it is the only type that can escape from inside the body to reach the detector, and it is weakly ionising so it does least damage on the way out.
   3. A tracer needs a short half-life, typically hours, so that it stops emitting soon after the scan and the patient is not irradiated for weeks.
   4. For treatment, a strong external beam of gamma is aimed at the tumour, and the high dose kills the rapidly dividing cancer cells.
   5. The beam is directed at the tumour from several different directions, so the tumour receives every dose while any one piece of healthy tissue is only in the path once.