The relation between the mean life time $\tau$ and the half life time $\mathrm{T}_{1 / 2}$ of a radioactive…

The relation between the mean life time $\tau$ and the half life time $\mathrm{T}_{1 / 2}$ of a radioactive substance is
  1. $\mathrm{T}_{1 / 2}=\tau \log _{\mathrm{e}} 2$
  2. $\mathrm{T}_{1 / 2}=\tau \log _{10} 2$
  3. $\mathrm{T}_{1 / 2}=\tau$
  4. $\mathrm{T}_{1 / 2}=2 \tau \log _{\mathrm{e}} 2$

Solution

Half life time $\mathrm{T}_{1 / 2}=\frac{\operatorname{iog}_{\mathrm{e}} 2}{\lambda}$ and mean life time $\mathrm{T}=\frac{1}{\lambda} \therefore \mathrm{T}_{1 / 2}=\mathrm{T} \log _{\mathrm{e}} 2$

Asked in: AP EAMCET 2023 (15 May Shift 1)

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