AP EAMCET · PHYSICS · Nuclear Physics
The relation between the mean life time \(\tau\) and the half life time \(\mathrm{T}_{1 / 2}\) of a radioactive substance is
- A \(\mathrm{T}_{1 / 2}=\tau \log _{\mathrm{e}} 2\)
- B \(\mathrm{T}_{1 / 2}=\tau \log _{10} 2\)
- C \(\mathrm{T}_{1 / 2}=\tau\)
- D \(\mathrm{T}_{1 / 2}=2 \tau \log _{\mathrm{e}} 2\)
Answer & Solution
Correct Answer
(A) \(\mathrm{T}_{1 / 2}=\tau \log _{\mathrm{e}} 2\)
Step-by-step Solution
Detailed explanation
Half life time \(\mathrm{T}_{1 / 2}=\frac{\operatorname{iog}_{\mathrm{e}} 2}{\lambda}\) and mean life time \(\mathrm{T}=\frac{1}{\lambda} \therefore \mathrm{T}_{1 / 2}=\mathrm{T} \log _{\mathrm{e}} 2\)
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