(B) The radioactive decay follows the formula: $N = N_0 \times (\frac{1}{2})^n$,where $n$ is the number of half-lives.Given that the radioactivity is

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(B) The radioactive decay follows the formula: $N = N_0 \times (\frac{1}{2})^n$,where $n$ is the number of half-lives.Given that the radioactivity is half of the fresh wood,we have $\frac{N}{N_0} = \frac{1}{2}$.Substituting this into the equation: $\frac{1}{2} = (\frac{1}{2})^n$,which implies $n = 1$.The age of the sample $(t)$ is calculated as $t = n \times t_{1/2}$.Given $t_{1/2} = 6000 \ years$,we get $t = 1 \times 6000 = 6000 \ years$.

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

Medium

The radioactivity due to the $^{14}C$ isotope (half-life $6000 \ years$) of a sample of wood from an ancient tomb was found to be nearly half that of fresh wood. The tomb is therefore about ........... years old.

A
$3000$
B
$6000$
C
$9000$
D
$1200$

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Nuclear Chemistry

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Rate of decay and Half-life

$8 \ g$ of a radioactive substance is reduced to $0.5 \ g$ after $1 \ hour$. The ${t_{1/2}}$ of the radioactive substance is ......... $\min$.

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$A$ radioactive isotope having a half-life of $3 \ days$ was received after $12 \ days$. It was found that there were $3 \ g$ of the isotope in the container. The initial weight of the isotope when packed was ......... $g$.

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If the quantity of a radioactive element is doubled,then its rate of disintegration per unit time will be

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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 $...... \, \text{min}$.

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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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The radioactivity due to the $^{14}C$ isotope (half-life $6000 \ years$) of a sample of wood from an ancient tomb was found to be nearly half that of fresh wood. The tomb is therefore about ........... years old.

Similar Questions

$8 \ g$ of a radioactive substance is reduced to $0.5 \ g$ after $1 \ hour$. The ${t_{1/2}}$ of the radioactive substance is ......... $\min$.

$A$ radioactive isotope having a half-life of $3 \ days$ was received after $12 \ days$. It was found that there were $3 \ g$ of the isotope in the container. The initial weight of the isotope when packed was ......... $g$.

If the quantity of a radioactive element is doubled,then its rate of disintegration per unit time will be

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 $...... \, \text{min}$.

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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