(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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Rate of decay and Half-life

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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 decay constant of a radioactive element is $3 \times 10^{-6} \ min^{-1}$. Its half-life is

$A$ radioactive sample $(Z = 22)$ decreases by $90\%$ in $10 \ \text{years}$. What will be the half-life of the sample in $\text{years}$?

If the half-life of a substance is $5 \, \text{years}$,then the total amount of substance left after $15 \, \text{years}$,when the initial amount is $64 \, \text{grams}$,is ....... $\text{gm}$.

The half-life of a radioactive element is $6 \ months$. The time taken to reduce its original concentration to its $1/16$ value is ....... $years$.

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