Question

Derive an expression for half life period of a radioactive substance

Answer 1

half life of a radioactive substance, i.e the time taken for half the nuclei present to disintigrate

radioactive decay is governed by the equation: Nt = No e –λt

(1) Where Nt is the count at time, No is the initial concentration (at time 0), and λ is the constant called the decay constant which is different for each radioactive nuclide

[3]. At the half-life of the radioactive isotope, Nt = Nt½ = ½ No (2)

And

substituting equation (2) into equation (1) gives: No/2 = No e –λ t½ (3)

Where t½ is the half-life period for the decay process. Further simplification of equation (3) gives: ½ = e –λ t½

(4) Taking natural logarithm of both sides of the equation: ln ½ = -λt½

(5) -0.693 = -λt½

(6) t½ = 0.693/ λ