Radioactive Activity
Decays per second in a sample.
Formula
Variables
How it works
Radioactive activity is the rate at which nuclei in a sample decay, measured in decays per second (becquerels). The formula A = λN works because each nucleus has the same constant probability per unit time of decaying, so a larger number of undecayed nuclei produces more decays each second. The decay constant λ tells you how likely one nucleus is to decay in one second, and multiplying by N gives the total expected decay rate for the whole sample.
When to use it
Use this when you need the current activity of a radioactive source from the number of nuclei present and the isotope’s decay constant. It is also useful for converting between activity, half-life, and remaining quantity in nuclear physics, radiometric dating, and medical isotopes.
Worked example, step by step
A sample contains N = 8.0 × 10^12 undecayed nuclei of a radioactive isotope. The decay constant is λ = 3.5 × 10^-5 s^-1. Use A = λN. A = (3.5 × 10^-5 s^-1)(8.0 × 10^12) A = 2.8 × 10^8 s^-1 So the activity is 2.8 × 10^8 Bq, meaning about 280 million decays per second.
Common mistakes to avoid
- Using the half-life directly instead of converting it to λ first
- Forgetting that activity is in decays per second, so the unit is Bq
- Using the total original number of nuclei instead of the number still undecayed
Did You Know?
The becquerel, one decay per second, is such a tiny unit that a banana registers about fifteen of them.
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