Question

Define the terms (i) half-life (T_1/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).

Answer 1

Half-life
The half-life of a radioactive substance is defined as the average time for which the nuclei of the atoms of the radioactive substance exist.

`t = t_(1/2)`

`R =1/2R_0`

`∴ t_(1/2)=(1n2)/λ`

`=(0.693)/4`

Average life or mean-life (τ):

`tau``=(λN_0int_0^oo te^(-λ1)dt)/N_0`

= `λint_0^oo te^(-λ1)dt`

`tau=1/lambda`

`∴ T_(1/2)=(1n2)/λ = tau 1n2`