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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

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 =  = 0.25 = 4.2 × 10-12 s-1 N 6 × 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%

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 =  = 0.25 = 4.2 × 10-12 s-1 N 6 × 10 10

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%

EXPLAIN… N = N0e-t

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)

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

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.

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

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

y-intercept = N0 Gradient = -

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?

Plenary 1 Peer Mark Feed back

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