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  4. The activity of a radioactive substance falls to 87.5 % of the initial value in 5 years. What is the half-life of the element ?

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Q. The activity of a radioactive substance falls to $ 87.5\% $ of the initial value in $ 5 $ years. What is the half-life of the element ?

UPSEEUPSEE 2006

Solution:

$\because \lambda = \frac{2.303}{t} log \frac{N_{0}}{N}$
Here $t= 5$ years, $ N_{0} = 100, N = 87.5 $
$ \therefore \lambda = 0.0267 $year$^{-1} $
$ \because t_{12}=\frac{0.693}{\lambda} = \frac{0.693}{0.0267} = 25.95$ years
$\approx 26$ years