(B) For a first-order reaction,the amount remaining after $n$ half-lives is given by $N = N_0 \times (1/2)^n$. Given that the substance reduces to $1/

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(B) For a first-order reaction,the amount remaining after $n$ half-lives is given by $N = N_0 \times (1/2)^n$. Given that the substance reduces to $1/16$ of the original amount,we have $1/16 = (1/2)^n$. Since $1/16 = (1/2)^4$,it follows that $n = 4$ half-lives. The total time taken is $2 \, \text{hours} = 120 \, \text{min}$. Therefore,$4 \times t_{1/2} = 120 \, \text{min}$. $t_{1/2} = 120 / 4 = 30 \, \text{min}$.

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

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After $2 \, \text{hours}$,the amount of a certain radioactive substance reduces to $1/16^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is $...... \, \text{min}$.

KVPY 2011 All KVPY

A
$15$
B
$30$
C
$45$
D
$60$

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Nuclear Chemistry

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Rate of decay and Half-life

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KVPY 2011 Paper All KVPY years →

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If the disintegration constant is $6.93 \times 10^{-6} \ s^{-1}$,then the half-life of $_{6}C^{14}$ will be:

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The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

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$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

Medium

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After $2 \, \text{hours}$,the amount of a certain radioactive substance reduces to $1/16^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is $...... \, \text{min}$.

Similar Questions

$^{18}_{8}O$ has a half-life of $4650 \text{ years}$. $200 \text{ mg}$ of a sample of $^{18}_{8}O$ is reduced to $25 \text{ mg}$ in ......... $\text{years}$.

For a radioactive substance with a half-life period of $500$ years,the time required for the complete decay of $100 \ mg$ of it would be:

If the disintegration constant is $6.93 \times 10^{-6} \ s^{-1}$,then the half-life of $_{6}C^{14}$ will be:

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

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