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  4. The half life of a radioactive substance is 20 minutes. The time taken between 50 % decay and 87.5 % decay of the substance will be

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Q. The half life of a radioactive substance is $20\, minutes$. The time taken between $50\%$ decay and $87.5\%$ decay of the substance will be

KCETKCET 2015Nuclei

Solution:

Given, $ T_{1 / 2}=20 \,min $
$N_{1}=50 $
$N_{2}=100-87.5=12.5$
We know that, time taken by a substance to decay,
$t_{2}-t_{1} =\frac{T}{\ln 2} \ln \left(\frac{N_{1}}{N_{2}}\right)=\frac{20}{\ln 2} \ln \left[\frac{50}{12.5}\right] $
$=\frac{20}{\ln 2} \ln 4=40 \,min$