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 = N
_{0}/2, to the x-axis, then repeating for N = N_{0}/4, N = N_{0}/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 0.5
^{n}= fraction remaining after n half-lives - This is the same as calculating 1/2
^{n} - Multiplying the fraction by the original number of nuclei will produce the remaining number
- The half-life t
_{1/2}and the decay constant are related by the equation: - t
_{1/2}= 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 = A
_{0}e^{-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 0.5
^{n} - 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=N
_{0}e^{-λt}is in the formula booklet, but you’ll have to remember that the same goes for using A instead of N

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