### Radioactivity was discovered by A.H. Becquerel 1896 accidently.

Radioactivity was a nuclear phenomenon in which an unstable nucleus undergoes decay. This is referred to as radioactive decay. Three types of radioactive decay occur in nature:

- α-decay in which a helium nucleus is emitted;
- β-decay in which electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of electron) are emitted;
- γ-decay in which high energy (hundreds of keV or more) photons are emitted.

### Law of Radioactive Decay:

In any radioactive sample, which undergoes α, β or γ-decay, it is found that the number of nuclei undergoing the decay per unit time is proportional to the total number of nuclei in the sample. If *N *is the number of nuclei in the sample and ∆*N *undergo decay in time ∆*t *then

where λ is called the radioactive decay constant or disintegration constant.

Also, N = N_{0} e^{-λt} , here N_{0} is the number of radioactive nuclei present initially.

### Radioactive Decay Constant:

As, N = N_{0} e^{-λt} , now, if we put t = 1/λ , we have, N = N_{0} e^{-1}

The radioactive decay constant can may be defined as the reciprocal of the time during which the number atoms is a radioactive substance reduces to 36.8% of their initial number.

### Half Life: Radioactive Substance

It is the time interval in which the mass of a radioactive substance or the number of its atoms is reduced to half of its initial value.

### Relation between Half Life and Decay constant

Half life (T_{1/2}) and decay constant (λ) are related as, T_{1/2} = 0.693/λ

### Activity of Radioactive Constant

Rate of disintegration or count rate of a sample of radioactive material is called activity and is directly proportional to the number of atoms of left undecayed in the sample

Activity A, |dN/dt| = λN

### Mean Life (or Average Life) of a Radioactive Substance

It is the average of the lives of all the atoms in a radioactive substance is called the ‘mean life’ or ‘average life’ of that substance.

The mean life (T) of a radioactive substance is equal to reciprocal of decay constant.

It means, T = 1/λ. Also, T = 1.443 T_{1/2}