﻿ Law of radioactivity

A radioactive material decays exponentially.

Although radioactivity is a random process, there is a certain underlying order to it.

The Half-life is the time taken for half the radioactive nuclei in a sample to decay.

The half-life is a constant value for a particular isotope ...

....it is indendent of the size of the sample or the time at which measurements are taken.

The rate of decay of a radioactive material is proportional to the number of undecayed atoms in the sample.

This may be expressed mathematically as shown:
dN/dt N

which may be written as
dN/dt = -N
The negative sign tells us that N diminishes as time passes.

of the random nature of radioactivity

Applying calculus to the above equation leads to the result:

This is an exponential equation. We may interpret the result in a number of ways:

 The number of radioactive nuclei present in a sample decreases exponentially with time The number of radioactive nuclei yet to decay is a fraction of the original number in the sample (since exp(-t) is less than 1)

Activity
Activity is the number of disintegrations per second which occur in a radioactive sample. It is a measure of the strength of the source. The SI unit of activity is the Bequerel (Bq).

Decay constant
This is the probability per second that a nucleus will disintegrate.

Half-life
Although radioactivity is a random process, there is an underlying order to it. It can be shown mathematically (and has been verified by experiment) that the time taken for half the radioactive nuclei in a sample to decay is a constant value. We call this time interval the Half-life, denoted by T.
It can be shown that T = 0.693/
By analysing the formula it can be seen that the value of T depends only on the decay constant and is therefore independent of the number of atoms present N, or the time t, at which the measurements were taken.