Radioactivity - Notes | Study Physics Class 12 - NEET

Radioactivity

The phenomena of disintegration of heavy elements into comparatively lighter elements by the emission of radiations is called radioactivity. This phenomena was discovered by Henry Becquerel in 1896.

Radiations Emitted by a Radioactive Element

Three types of radiations emitted by radioactive elements

(i) α-rays

(ii) β-rays

(iii) γ – rays

α-rays consists of α-particles, which are doubly ionised helium ion.

β-rays are consist of fast moving electrons.

γ – rays are electromagnetic rays.

When an α – particle is emitted by a nucleus its atomic number decreases by 2 and mass number decreases by 4.

When a β -particle is emitted by a nucleus its atomic number is Increases by one and mass number remains unchanged.

When a γ – particle is emitted by a nucleus its atomic number and mass number remain unchanged

Radioactive Decay law

The rate of disintegration of radioactive atoms at any instant is directly proportional to the number of radioactive atoms present in the sample at that instant.

Rate of disintegration (– dN / dt) ∝ N

– dN / dt = λ N

where λ is the decay constant.

The number of atoms present undecayed in the sample at any instant N = N_o e^-λt

where, N_o is number of atoms at time t = 0 and N is number of atoms at time t.

Half-life of a Radioactive Element

The time is which the half number of atoms present initially in any sample decays, is called half-life (T) of that radioactive element.

Relation between half-life and disintegration constant is given by

T = log²_e / λ = 0.6931 / λ

Average Life or Mean Life(τ)

Average life or mean life (τ) of a radioactive element is the ratio of total life time of all the atoms and total number of atoms present initially in the sample.

Relation between average life and decay constant τ = 1 / λ

Relation between half-life and average life τ = 1.44 T

The number of atoms left undecayed after n half-lives is given by

N = N_o (1 / 2)ⁿ = N_o (1 / 2) ^t/T

where, n = t / T, here t = total time.

Activity of a Radioactive Element

The activity of a radioactive element is equal to its rate of disintegration.

Activity R = (– dN / dt)

Activity of the sample after time t,

R = R_o e ^-λt

Its SI unit is Becquerel (Bq).

Its other units are Curie and Rutherford.

1 Curie = 3.7 * 10¹⁰ decay/s

1 Rutherford = 10⁶ decay/s