#### Question

Define the terms (i) half-life (T_{1}_{/2}) and (ii) average life (τ). Find out their relationships with the decay constant (λ).

#### Solution

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`

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Solution Define the Terms (I) Half-life (T1/2) and (Ii) Average Life (τ). Find Out Their Relationships with the Decay Constant (λ). Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy.