Half-life Relation

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Half-life T_{1/2} relates to decay constant by:

RankGuru · Accepted Answer

The half-life ($T_{1/2}$) is the time taken for the number of radioactive nuclei to reduce to half of its initial value ($N = N_0/2$). Substituting this into the decay equation $N = N_0 e^{-\lambda t}$ gives:
$N_0/2 = N_0 e^{-\lambda T_{1/2}}$
$1/2 = e^{-\lambda T_{1/2}}$
$\ln(1/2) = -\lambda T_{1/2}$
$T_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}$.

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Half-life Relation

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