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  3. Chemistry
  4. During the nuclear explosion, one of the products is 90Sr with half life of 6.93 years. If 1 μg of 90Sr was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically . Given 9.9

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Q. During the nuclear explosion, one of the products is $^{90}Sr$ with half life of 6.93 years. If 1 $\mu$g of $^{90}Sr$ was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically __________.
Given 9.9

JEE MainJEE Main 2020Chemical Kinetics

Solution:

$k =\frac{0.693}{ t _{1 / 2}}$
$=\frac{0.693}{6.93}=0.1 year ^{-1}$
$t =\frac{2.303}{ k } \log \left(\frac{ R _{0}}{ R _{ t }}\right)$
$R _{0}=1 \mu g$
$R _{ t }=1-1 \times \frac{90}{100}$
$=0.1 \mu g$
$=\frac{2.303}{0.1} \log \left(\frac{1}{0.1}\right)$
$=23.03 years$