(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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Class 12

Chemistry Questions

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Nuclear Chemistry

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Rate of decay and Half-life

The half-life of an isotope is $10 \ hrs$. How much will be left behind after $4 \ hrs$ in a $1 \ gm$ sample? (Assume the molar mass of the isotope is $1 \ g/mol$ for calculation purposes).

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The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

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

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The half-life of $C^{14}$ is $5760 \ years$. For a $200 \ mg$ sample of $C^{14}$, the time taken to change to $25 \ mg$ is (in $years$)

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The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

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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

The half-life of an isotope is $10 \ hrs$. How much will be left behind after $4 \ hrs$ in a $1 \ gm$ sample? (Assume the molar mass of the isotope is $1 \ g/mol$ for calculation purposes).

The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

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

The half-life of $C^{14}$ is $5760 \ years$. For a $200 \ mg$ sample of $C^{14}$, the time taken to change to $25 \ mg$ is (in $years$)

The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

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