(C) All nuclear decays follow first-order kinetics.$t = \frac{1}{k} \ln \frac{[A_0]}{[A]}$Given $t_{1/2} = 6.93 \; \text{years}$,so $k = \frac{0.693}{

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(C) All nuclear decays follow first-order kinetics.$t = \frac{1}{k} \ln \frac{[A_0]}{[A]}$Given $t_{1/2} = 6.93 \; \text{years}$,so $k = \frac{0.693}{t_{1/2}} = \frac{0.693}{6.93} = 0.1 \; \text{year}^{-1}$.To reduce it by $90 \%$,the remaining amount $[A] = 10 \% \text{ of } [A_0] = 0.1 [A_0]$.$t = \frac{2.303}{k} \log_{10} \frac{[A_0]}{0.1 [A_0]} = \frac{2.303}{0.1} \log_{10} (10) = 23.03 \times 1 = 23.03 \; \text{years}$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. 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?

JEE MAIN 2020 All JEE MAIN

A
$27.01$
B
$25.07$
C
$23.03$
D
$21.06$

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During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. 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?

Similar Questions

The half-life period for a radioactive substance is $15$ minutes. How many grams of this radioactive substance is decayed from $50$ g of substance after $1$ hour?

$8 \, g$ of the radioactive isotope,cesium$-137$ were collected on February $1$ and kept in a sealed tube. On July $1$,it was found that only $0.25 \, g$ of it remained. So the half-life period of the isotope is ....... $days$.

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Assuming $1 \, \mu g$ of trace radioactive element $X$ with a half-life of $30 \ years$ is absorbed by a growing tree. The amount of $X$ remaining in the tree after $100 \ years$ is $n \times 10^{-1} \, \mu g$. Find the value of $n$. $[Given : \ln 10 = 2.303 ; \log 2 = 0.30]$

If a substance with a half-life of $3 \ days$ is kept for $12 \ days$,what fraction of the substance remains?

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