The decay process of radioactive elements is subject to the law of chance.
The probability of an atom disintegrating in any time interval is indenpendent of its past history and is the same for all atoms of the same kind.
Let N is the total number of the atom, dN is the number of atom distingegrating in time interval dt
(dN/N)/dt = -p where p is the probability that decay will occurs.
so dN/N = -p dt
then we will have
N = No e-pt = No e-t/T where p=1/T
Nois the number of atoms at t=0, at t=T (called mean lifetime) N(T)=No e-1
We also define half-life T1/2 such that N(T1/2)=No/2
so T1/2 = log(2.) T = 0.693 T

A given radioactive decay can be a single step in a long sequence of transformation from one unstable nuclide to another.
There are three naturally occuring radioactive series beginning with 238U, 235U, and 232Th , all ending in different isotopes of lead.

For example: nuclide A will decay and become nuclide B, and nuclide B will decay and become nuclide C, ...

This applet will show how the population of each nuclide changed during radioactive decay series:

The applet shown radioactive decay from nuclide A(black) -> B(red) -> C(green) -> D(yellow).
Each circle represent a nuclide.

For example:

For nuclide A decay into nuclide B : black circle will change into red circle.
For nuclide A decay into nuclide B : red circle will change into green circle.
...
You can change decay time for each nuclide and see how the population for each nuclide change with time.

If you just want to see decay from A to B, and B is stable nuclide -> click the checkbox at the top-right.

`Author¡GFu-Kwun Hwang, Dept. of physics, National Taiwan Normal University`