Activity & Half-Life
- The activity of a radioactive sample is defined as:
The number of nuclei which decay in a given time
- Activity is measured in becquerels (Bq)
- One becquerel is equivalent to a nucleus decaying every second
- It is impossible to know when a particular unstable nucleus will decay
- But the rate at which the activity of a sample decreases can be predicted
- This is known as the half-life
- Half-life is defined as:
The time taken for half the undecayed nuclei to decay or the activity of a source to decay by half
- In other words, the time it takes for the activity of a sample to fall to half its original level
- Different isotopes have different half-lives and these can vary from a fraction of a second to billions of years in length
Using Half-life
- Scientists can measure the half-lives of different isotopes accurately:
- Uranium-235 has a half-life of 704 million years
- This means it would take 704 million years for the activity of a uranium-235 sample to decrease to half its original amount
- Carbon-14 has a half-life of 5700 years
- So after 5700 years, there would be 50% of the original amount of carbon-14 remaining
- After two half-lives, or 11 400 years, there would be just 25% of the carbon-14 remaining
- With each half-life, the amount remaining decreases by half
Graph showing how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed
- The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life
- It is the same length of time as it would take to decrease from 50 % activity to 25 % activity
- The half-life is constant for a particular isotope
- The following table shows that as the number of half-life increases, the proportion of the isotope remaining halves
Worked example
A radioactive sample has a half-life of 3 years. What is the ratio of decayed nuclei to original nuclei, after 15 years?
Answer:
Step 1: Calculate the number of half-lives
- The time period is 15 years
- The half-life is 3 years
half-life = 15 / 3 = 5
- There have been 5 half-lives
Step 2: Raise 1/2 to the number of half-lives
- The proportion of nuclei remaining is
(1/2)5 = 1/32
- So 1/32 of the original nuclei are remaining
Step 3: Write the ratio correctly
- If 1/32 of the original nuclei are remaining, then 31/32 must have decayed
- Therefore, the ratio is 31 decayed : 32 original, or 31:32
Worked example
A particular radioactive sample contains 2 million un-decayed atoms. After a year, there are only 500 000 atoms left un-decayed.
Determine the half-life of the material.
Answer:
Step 1: Calculate how many times the number of un-decayed atoms has halved
- There were 2 000 000 atoms to start with
- 1 000 000 atoms would remain after 1 half-life
- 500 000 atoms would remain after 2 half-lives
- Therefore, the sample has undergone 2 half-lives
Step 2: Divide the time period by the number of half-lives
- The time period is a year
- The number of half-lives is 2
- 1 year divided by 4 (22) is a quarter of a year or 3 months
- Therefore, the half-life of the sample is 3 months
Determine the half-life of this material.
