1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.

Equations

The activity (A) of a radioactive sample (the number of decays per unit time) is found to be proportional to the number of radioactive nuclei (N) in a given sample. That is,

$$A = - \frac{dN}{dt} = \lambda N$$

Where $\lambda$ is the constant of proportionality and is called the decay constant. The above expression is a separable ODE and has a solution,

$$A = A_0e^{-\lambda t}$$

Where $A_0$ represents the initial activity of the sample at t=0. Equivalently, one can form an expression for the number of remaining radioactive nuclei,

$$N = N_0e^{-\lambda t}$$

Where $N_0$ represents the initial number of radioactive nuclei at t=0.

Extended explanation

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