Half-LifeCambridge IGCSE Physics: Revision notes
Section 1
Background radiation
Background radiation is the ionising radiation that is present all the time, everywhere, from a range of sources:
- Radon gas in the air
- Rocks and buildings
- Food and drink
- Cosmic rays from space
Any measurement of radioactivity from a sample must take background radiation into account, since the detector will always register some counts even with no sample present.
Section 2
Measuring count rate
Ionising radiation can be measured using a detector connected to a counter, giving a count rate — typically in counts per second or counts per minute.
Because background radiation is always present, a raw count rate from a radioactive sample includes both the sample's own radiation and the background. To find the corrected count rate (the count rate due to the sample alone):
corrected count rate = measured count rate minus background count rate
This correction must always be applied before using the data to find a half-life.
Always subtract background radiation before calculating a half-life from a decay curve or table — using the raw, uncorrected count rate gives the wrong answer.
Section 3
Defining half-life
The half-life of a radioactive isotope is the time taken for half the nuclei of that isotope in any sample to decay. Equivalently, it is the time taken for the count rate (or activity) of a sample to fall to half its original (corrected) value.
Half-life is a fixed, characteristic property of each isotope — it does not depend on the amount of sample present, and it reflects the random nature of radioactive decay (you cannot know when an individual nucleus decays, but a large enough sample decays at a statistically predictable rate).
If a sample starts with a corrected count rate of 800 counts/minute and has a half-life of 10 minutes, after 10 minutes it falls to 400, after 20 minutes to 200, and so on.
Section 4
Calculating half-life from data or graphs
Half-life can be determined from a table of readings or from a decay curve (a graph of corrected count rate or activity against time):
- Identify the starting (corrected) count rate
- Find the time taken for the count rate to fall to half of that value
- That time interval is the half-life
- As a check, the count rate should fall by half again over the next equal time interval
If the data given has not already had background radiation subtracted, it must be corrected first before this method is applied.
Section 5
Choosing isotopes for applications by half-life and radiation type
The choice of isotope for a practical use depends on both the type of radiation it emits and its half-life:
| Application | Radiation needed | Half-life needed |
|---|---|---|
| Household smoke alarms | Alpha (ionises air in a small chamber) | Long, so it doesn't need frequent replacing |
| Irradiating food to kill bacteria | Gamma (penetrates deep into food) | — |
| Sterilising equipment | Gamma (penetrates packaging) | — |
| Measuring/controlling material thickness | Beta or gamma, chosen by how much the radiation should penetrate the material | Long, so the source's output stays roughly constant during use |
| Diagnosis and treatment of cancer | Gamma (penetrates to reach or exit the body) | Short enough to limit patient exposure after use |
For each application, always justify both the radiation type (based on penetrating power needed) and the half-life (based on how long the source needs to remain useful, or how quickly it should stop being active).
Must Know
- Background radiation comes from radon gas, rocks/buildings, food/drink and cosmic rays, and is always present
- Corrected count rate = measured count rate minus background count rate
- Half-life is the time for half the nuclei in a sample to decay (or for count rate/activity to halve)
- Half-life can be found from a table or decay curve; always correct for background radiation first if it hasn't been subtracted
- Isotope choice for an application depends on both radiation type (penetrating power) and half-life (how long it needs to remain useful)
- Long half-lives suit long-term uses (smoke alarms, thickness gauges); short half-lives suit uses needing quick decay (medical treatment)
That's the notes covered.
Carry on to the next subtopic.