2. We have learnt about three ways of measuring radioactivity:
Half life
Decay Constant
Activity
For each one, decide with your partner what it means and decide on which one is most useful in explaining how radioactive something is when:
You are explaining it to someone who is not a physicist
You are trying to work out how radioactive something will be in the future
You are telling a doctor about how much radiation someone might have absorbed

3. Favourite exam board tricks: Can you do these two
Favourite exam board tricks: Can you do these two? What are the potential pitfalls?
1. A radioactive isotope is made of 6 × 1010 atoms. It has a current activity of 0.25 Bq. What is the decay constant?
A = N
A =  = = 4.2 × s-1
N × 10 10
2. A radioactive isotope has a decay constant of 0.1 s-1 . What percentage of radioactive atoms remain after 15 seconds?
N=No e-t
N = e-t N0
= e – 0.1 × 15
= 0.22 = 22%

4. Favourite exam board trick 1:
A radioactive isotope is made of 6 × 1010 atoms. It has a current activity of 0.25 Bq. What is the decay constant?
A = N
A =  = = 4.2 × s-1
N × 10 10

5. Favourite exam board trick 2:
A radioactive isotope has a decay constant of 0.1 s-1 . What percentage of radioactive atoms remain after 15 seconds?
Nasty because it doesn’t tell you how many atoms there are to start with.
N=No e-t
N = e-t N0
= e – 0.1 × 15
= 0.22 = 22%

6. EXPLAIN…
N = N0e-t

7. N = N0e-t Decay constant in s-1 Time in s
Nuclei left undecayed (no unit)
Minus because it is decay
Nuclei at start (t=0) (no unit)

8. N = N0e-t Gives a graph like this:
Question: How can I work out  from this?

9. N = N0e-t (Apart from finding the half life and converting)
It is not obvious how to do it.
As a curve it is difficult to read, to project forward or backwards with accuracy.
We can turn the equation into a straight line by taking natural logs.

10. Solving for λ and t? N = N0e-t ln ex = x
Take natural logs of both sides.
ln N = ln (N0e -λt)
LOG RULES: ln (AB) = ln A + ln B
So, we end up with...
ln N = ln (N0) + ln (e -λt)
ln N = ln N0-t

11. ln N = ln N0-t
ln N = -t + ln N0
y = m x c

12. y-intercept = N0
Gradient = -

13. Going back to your dice model…
Grade
Outcome
Task E
I can use A=N
Work out the ‘activity’ (rate of change) at 6 throws C
I can use the concept of ratios with the equations and use the logarithm form
Calculate the percentage of dice expected to be remaining after 6 seconds. Check this against your graph.
Take logs of the number remaining column and draw a ln (number) against time graph.
Find  and check it against your value calculated last week from half lives A
I can prove an exponential relationship by taking logarithms
How does this graph help give a clearer picture of the extent that the dice showed an exponential relationship?

14. Plenary 1
Peer Mark
Feed back

15. I can show my understanding of effects ideas and relationships…
Plenary 2
Learning Review – use the tick sheet to grade yourself – today we did the statements:
I can show my understanding of effects ideas and relationships…
Radioactive decay modelled as an exponential relationship between the number of undecayed atoms, with a fixed probability of random decay per unit time
I can use the following words and phrases accurately…
For radioactivity: half-life, decay constant, random, probability
relationships of the form dx/dy = –kx , i.e. where a rate of change is proportional to the amount present
I can sketch, plot and interpret graphs of:
Radioactive decay against time
I can make calculations and estimates making use of:
iterative numerical or graphical methods to solve a model of a decay equation