1. Radioactive decay
State that radioactive decay is a random process, governed by probability
Define ‘half life’ and ‘activity’
Carry out calculations involving half life and activity.

3. From GCSE
Radioactive elements spontaneously break down. They release alpha, beta or gamma radiation or a combination of the above. Some decay more quickly than others.

4. Sketch a graph of N vs time
Mark on the graph the half life.

5. Half life Define ‘half life’ and ‘activity’
“The time taken for the number of nuclei in a sample to decay to half the original number.”

6. Sketch a graph of N vs time

7. State that radioactive decay is a random process, governed by probability
With one dice, I have no idea how many times I will get a ‘6’ if I throw it a few times. If I throw it many times, it becomes much more predictable… If I have 1015 dice, this will become incredibly predictable. Small variations make very little difference to the outcome.

8. In our ‘experiment’ the dice represent radioactive nuclei
In our ‘experiment’ the dice represent radioactive nuclei. Each time we throw the dice this represents on interval of time. The probability of any once nuclei decaying is 1/6 – when the dice lands ‘6’ up.

9. State that radioactive decay is a random process, governed by probability
N - expected
N - actual
144 1
120
124 2
100
101 3
83.3 87 4
69.4 69 5
57.9 55

10. Half life – seems to lie between three and four throws.

11. Data Fill in the table provided.
Plot a graph of N vs t for the actual results obtained.
Plot a graph of ln N vs t for the actual results obtained.
Calculate the gradient of the line.

13. The more dice were present, the greater the number of dice that we rolled a 6 on. The greater the number of radioactive nuclei present, the greater the number that decay in a given time interval.

14. Activity
The number of decays per unit time. A = - λ N Where λ is the decay constant. (The gradient of the graph we have just drawn.)

15. Carry out calculations involving half life and activity.
Half life is equal to natural log of 2 divided by the decay constant. t ½ = ln 2 / λ Use this equation to show that the half life of the dice is between 3 and 4 throws.

16. Carry out calculations involving half life and activity
A sample of an isotope has a half life of 500 s.
Calculate the decay constant.
What percentage remains after a time of
500s
250s
138s

17. Carry out calculations involving half life and activity
Iodine 131 is an isotope used in nuclear medicine. It has a half life of 8 days.
Calculate the number of nuclei of I-131 in 0.1 mg.
Calculate the decay constant for I-131.
Calculate the activity of 0.1 mg of I-131.
Calculate the activity remaining in the patient after 3 weeks.

18. Example
Cs-137 has a half life of about 30 years. Calculate the activity of 10g of pure Cs-137. It is considered ‘expired’ when activity of the sample has fallen to 1% of the original value. How long will this take?