Radioactive Decay

Radioactive decay is random and spontaneous.

The disintegration of an unstable nucleus cannot be predicted. Nor can it be influenced directly by e.g. heating the substance.
However, every nucleus has the same probability that it will decay in any given time interval. Therefore the number of nuclei that will decay in any given time can be predicted as it is proportional to the total number of nuclei present.
Let λ be a constant, called the decay constantLet N be the number of nuclei present at any one instant.The rate of decay/disintegration can be given by:

          ΔN/Δt = -λN        

where activity

A= λN

This is an exponential function which integrated gives us:

N = N₀e^-λt