Radioactive Decay (Part Two) – A2 Physics Revision

Make sure you’ve read the previous part of this post first!

Half Life

  • The half-life of a radioactive substance is the time taken for half of it to decay
  • The number of not-yet-decayed nuclei will always halve after this amount of time (unless the sample size is unreasonably small)
  • Since elements vary in how quickly they decay, half-life can be measured in a variety of units of time, such as milliseconds or years
  • That said, the units of the decay constant will depend on it (as the units on each side have to match in the equation at the end of this list)
  • You can see half-lives on the graph by drawing a line down from the point on the exponential curve where N = N0/2, to the x-axis, then repeating for N = N0/4, N = N0/8 and so on
  • The vertical distances between the points will be smaller each time, but the horizontal distance – the half-life – will be the same between each
  • To find the fraction of the nuclei which will be left after a given number of half-lives, you can use 0.5n = fraction remaining after n half-lives
  • This is the same as calculating 1/2n
  • Multiplying the fraction by the original number of nuclei will produce the remaining number
  • The half-life t1/2 and the decay constant are related by the equation:
  • t1/2 = ln(2) / λ

Using Activity Instead

  • Radioactive decay is exponential, so its rate of change is proportional to the quantity (of nuclei) present
  • This can be written as dN/dt α N
  • Counting the number of nuclei in a sample is very difficult, so it’s impractical to measure N
  • Since they’re proportional, dN/dt is often used in graphs and equations instead of N
  • The proper name for dN/dt is the activity and its symbol is A
  • A = dN/dt
  • The activity of a sample is the rate sample’s rate of decay
  • In other words, it’s the count rate; the number of radioactive emissions per unit time
  • As discussed for half-life, above, time could be measured in a variety of units
  • When you use A instead of N in the exponential equation, you get: A = A0e-λt
  • This graph is more practical to produce as A is much easier to measure than N
  • Activity is measured in counts per second. An equivalent unit is Bq (Becquerels)
  • The constant of proportionality between A and N is the decay constant, so:
  • A = dN/dt = λN
  • dN/dt will be negative as N is decreasing with time, but A, λ and N are all positive, so strictly there should be a minus sign in the equation for it to be true

Data, Formulae and Relationships Booklet

  • You’ll have to remember that the fraction after n half-lives is 0.5n
  • The equation relating half-life and decay constant is in the formula booklet
  • ΔN/Δt = -λN is in the formula booklet, but you’ll have to remember that this it’s also the activity, A
  • N=N0e-λt is in the formula booklet, but you’ll have to remember that the same goes for using A instead of N

About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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