Activity and the Decay Constant

Activity and the Decay Constant

These equations often confuse students but they are actually based on a few very simple ideas. Understand those and it all becomes easier.

1. Radioactive decay is a random, spontaneous event and cannot be predicted. However, if there are many of these decays, then the rate of decay can be predicted using statistics as described in the decay equations.

2. The number of decays you will measure each second (the activity, A) from a sample depends on the number of atoms in the sample, N.


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Here are two blocks of exactly the same radioisotope. The chance of an atom decaying from one is exactly the same as in the other but there are twice as many atoms in the 2kg block. So there will be twice as many decays per second in the 2kg block.

Note that the activity of a sample is measured in bequerel, Bq.

1Bq = 1 decay per second.

So in an equation this would be:

A ∝ N

A = λN


l = the constant of proportionality, called the Decay Constant.

Units: s-1, although sometimes quoted as hours -1 or even years -1.

The decay constant gives you an idea of how quickly or slowly a material will decay.

A large value of λmeans that the sample will decay quickly

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