# Radioactive Disintegration (Introduction to Radiochemistry)

Radioactive disintegration is a stochastic proces, which means a random process, that can be described statistically. In this task you will learn about the secular radioactive equilibrium, and how any measure of a radioactive source is stated with uncertainty.

In a sample with N radioactive atoms of a particular nuclide, the number of atoms that disintegrates with the time *dt *will be proportional with N, see the formula below.

,

where λ is the disintegration constant and A is the rate of disintegration.

The above equation can be solved into the following:

*N*_{t} = *N*_{0}*e*^{ - λt}

N_{0} is the number of atoms of the nuclide at hand present at t = 0. The time past when half of the nuclides has disintegrated is called the half-life.

*N = N _{0}/2* can be placed into equation 1.1 to give the following connection between the disintegration constant and the half-life:

The half-life is a characteristic value for each radioactive nuclide. A radioactive nuclide will often disintegrate into a product that is radioactive as well: Nucleus 1

Assume that at the time *t = 0*, N_{0 }of the mother is *N _{1}(t =0), N_{2}(t=0) and N_{3}(t=0)*, the change in number of mother- and daughter nuclides can then respectively be described through the following equations:

*dN _{1} = -λN_{1}dt*

*dN _{2} = λ_{1}N_{1}dt - λ_{2}N_{2}dt*

If the half-life of the mother is much less than that of the daughter, equation 1.2 can be simplified into:

where

is the saturation factor and