(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 radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

$A$ radioactive substance has a half-life $(t_{1/2})$ of $60 \ minutes$. After $3 \ hours$,what percentage of the radioactive substance will remain?

What is the half-life of a radioactive substance if $87.5\%$ of any given amount of the substance disintegrates in $40 \, min$?

Radioactivity of a sample $(Z=22)$ decreases by $90 \%$ after $10 \ years$. What will be the half-life of the sample (in $years$)?

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

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