12th physics. NCERT notes

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:

  1. α-decay in which a helium nucleus is emitted;
  2. 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;
  3. 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 = N0 e-λt , here N0 is the number of radioactive nuclei present initially.

Radioactive Decay Constant:

As, N = N0 e-λt , now, if we put t = 1/λ , we have, N = N0 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 (T1/2) and decay constant (λ) are related as, T1/2 = 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 T1/2

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