Radioactive decay is o spontaneous process. It goes on independent of external control, it is not affected by temperature, or pressure or by chemical treatment. It is a random process as no one can predict which atom will disintegrate at at a given time.
The radioactive decay law states that “the probability per unit time that a nucleus will decay is a constant, independent of time”.
The half-life of a radioactive element is the time taken for half of the atoms initially present in the element to decay. The rate of decay of radioactive elements is found to be proportional to the number of atoms of the material present. If there are N atoms of a radioactive element
‘present at a time, t, then the probable number of disintegration per unit time or activity is given by
N α – (dN/dt)
The minus sign arises from the fact that N is decreasing with time. The constant of proportionality (λ) is used to change the proportionality symbol to an equal sign. That is
λN = – (dN/dt)
λ = 1/N (dN/dt)
Decay constant is defined as the instantaneous rate of decay per unit atom of a substance
λ = number of atoms disintegrating per second/ number of atoms in the source at that time
time (t) = 0.693/λ