Radioactivity And The Law

M. Curie and P. Curie with Becquerel, were awarded the Nobel Prize in Physics for their discovery of Radioactivity, in 1903.

• When a nucleus undergoes alpha or beta decay, its atomic number Z changes and it becomes the nucleus of a different element.
• The energy liberated during radioactive decay comes from within individual nuclei without external excitation, similar to the case of atomic radiation.
• Radioactive decay is a statistical process that obeys the law of chance i.e. a certain probability per unit time.

Law of Radioactive Decay

1. Activity: The activity of a sample of any radioactive nuclide is the rate at which the nuclei of its constituent atoms decay.

R = - ^dN / _dt

1 becquerel = 1 B _q = 1 decay/s

1 curie = 1 Ci = 3.70 10 ¹⁰ decay/s = 37 GB _q

R = R ₀ e ^{- λ} t

2. Half-life: The half-life of a radioactive nuclide is defined as the time T _1/2 in which the actual amount of radioactive atoms is reduced by way of disintegration to half its value. After a half-life has elapsed when t = T _1/2 the activity R drops to 1/2 ^R ₀ . Hence,

1/2R ₀ = R ₀ e ^-λT _1/2

_e ^{- T} _1/2 = 2

T _1/2 = ln2/ = 0.693/ λ

dN = -N λ dt

3. Mean Life or Average life: The average or mean lifetime T of all atoms in a given sample is defined as the reciprocal of its decay probability per unit of time:

R = - dN/dt

R = N ₀ e ^{- λ t}