Half Life
Physics: AQA A Level, topic 8.1.5
Half-Life
Although each nuclear decay is random, with a large collection of nuclei, we can statistically predict how many will decay in a certain time.
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Time taken to halve
- Half-life, T1/2, is the time taken:
- For the number of radioactive nuclei in a sample to halve.
- For the activity (the number of decays per second) to halve.
Activity
- The activity of a sample is directly proportional to the number of nuclei remaining:
- Activity = decay constant, λ x number of nuclei remaining.
- Activity is related to half-life:
- = 0.69 ÷ T1/2
Activity 2
- By knowing the activity, we can infer how many nuclei are remaining.
- Knowing the atomic mass of an isotope and the mass of a sample of isotope enables the number of nuclei and so the activity to be found.
Example
- Find the half-life of a sample of plutonium-239, which has a mass of 1200 g and an activity of 2.8 × 1012 Bq:
- Number of moles of Pu-239 = 1200 ÷ 239 = 5.021.
- Number of nuclei = number of moles × Avogadro’s constant = 3.02 × 1024.
- λ = activity ÷ number of nuclei = 9.26 × 10-13.
- So, half-life T1/2 = ln(2) ÷ λ = 7.5 × 1011 s.
Half-Life
The half-life of a sample is the time taken for the number of radioactive counts to fall to half the initial value.
Half-life
- Half-life is the time taken for half of the sample to decay.
- This is the same as saying the time taken for the count rate to halve.
- Knowing the half-life of a substance and the number of nuclei it has means we can find its age.
Uses of half-life
- We can find the age of a material by considering the count rate of the material.
- By knowing the original count rate, the current count rate, and the half-life of the material - we can use the following equation to calculate the time passed:
Graphical Method
Half life can be found in many ways, the easiest is to use a graph.
Graphical method
- Firstly plot a graph of count rate or number of atoms against time.
- The plot should show exponential decay.
- Look for the initial count rate / number of atoms (the y-intercept).
Graphical method 2
- Divide the initial count rate or number of atoms by two, this is the half count rate, or half the initial number of atoms.
- Draw a line across from the half count rate to the decay curve.
- Draw a line down to the time axis (x axis) and read off the time. This is the half-life.
Graphical method 3
- Each half-life will be the same length.
- So it will take two half-lives for the sample to decay to a quarter of the initial count, or a quarter of the initial atoms.
Test yourself on Half Life
A radioactive sample initially weighs 4 g. After 2 half-lives, what is the mass of the radioactive sample?
What do half-lives allow us to do?
What equation can be used to calculate the age of an object?
Which of the following statements are true:
A) Half-life is the time taken for half of the nuclei to decay.
B) Half-life is the time taken for the count rate to halve.Finding half life using a graph