Half-Life (OCR GCSE Physics A, Combined (Gateway Science Suite)): Revision Notes
4.2.5 Half-Life
Half-Life
The half-life of an isotope is the time taken for half the nuclei in a sample to decay or the time taken for the activity or count rate of a sample to decay by half. It cannot be predicted when any one nucleus will decay, but the half-life is a constant that enables the activity of a very large number of nuclei to be predicted during the decay.
Example Calculation:
- If 80 atoms fall to 20 over 10 minutes, the half-life?
- – so two half-lives in 10 minutes
- So the half-life is 5 minutes
Characteristics of Half-Life:
- Short Half-Life:
- The source presents less of a risk, as it does not remain strongly radioactive.
- This means initially it is very radioactive, but quickly dies down.
- So presents less of a long-term risk.
- Long Half-Life:
- The source remains weakly radioactive for a long period of time.
- Example: Americium has a half-life of 432 years.
- It is an alpha emitter and is used in smoke alarms.
- It is emitted into the air around the alarm and does not reach far because alpha is weakly penetrating.
- If smoke reaches the alarm, the amount of alpha particles in the surrounding air drops.
- This causes the alarm to sound.
It is suitable because it will not need to be replenished, and its weak activity means it won't be harmful to anyone.
Net Decline
- Calculate the ratio of net decline of radioactive nuclei after X half-lives:
- Half the initial number of nuclei, and keep doing so X number of times.
Formula:
Half-Life
Radioactivity is a completely random process – unpredictable radiation given out by radioactive substances from the nuclei of their atoms can be measured with a Geiger-Muller tube and counter. This records the count rate = the number of radiation counts reaching it per second.
You can't predict which nucleus in a sample will decay next, but you can find out the time it takes for the amount of radiation emitted by a source to halve. This is known as the half-life. Half-life can be used to find a source's activity (Bq) – the rate at which it decays.
Key Terms
- Half-life:
- Time it takes for the amount of radiation emitted by a source to halve.
- Count-rate:
- Number of radiation counts reaching the Geiger-Muller tube per second.
- Activity (Bq):
- The rate at which a source decays (1 Bq = 1 decay/second).
Notes
- The radioactivity of a source decreases over time.
- Note: Activity never reaches zero.
- Half-life:
- Time taken for the number of radioactive nuclei in an isotope to halve (activity to fall to half its initial level).
Example Calculation
- Question:
- The initial activity of a sample is 640 Bq. Calculate the final activity as a percentage of the initial activity after 2 half-lives.
- Calculation:
- 1 half-life:
- 2 half-lives:
Radioactive Isotopes and Half-Life
Radioactive Isotopes
- Release radiation from the nucleus of their atoms.
- Decay is a random process.
Half-Life
- The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve.
- The half-life is also the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.
Example Calculation
- Question: A radioactive isotope has a half-life of 15 days and an initial count rate of 200 counts per second. Determine the count rate after 45 days.
- Start: 200 counts/s
- 15 days: 100 counts/s
- 30 days: 50 counts/s
- 45 days: 25 counts/s