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Question
Define the terms (i) half-life (T1/2) 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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