(A) The radioactive decay follows the formula: $\frac{N}{N_0} = (\frac{1}{2})^{\frac{T}{t_{1/2}}}$.Given $\frac{N}{N_0} = 0.13$ and $t_{1/2} = 5770 \

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(A) The radioactive decay follows the formula: $\frac{N}{N_0} = (\frac{1}{2})^{\frac{T}{t_{1/2}}}$.Given $\frac{N}{N_0} = 0.13$ and $t_{1/2} = 5770 \ years$.Taking the logarithm on both sides: $\log(0.13) = \frac{T}{5770} \times \log(0.5)$.$-0.886 = \frac{T}{5770} \times (-0.301)$.$T = \frac{0.886 \times 5770}{0.301} \approx 16975 \ years$.Rounding to the nearest provided option,the age is approximately $16989 \ years$.

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

Difficult

The $C^{14}$ to $C^{12}$ ratio in a wooden article is $13\%$ that of the fresh wood. Calculate the age of the wooden article. Given that the half-life of $C^{14}$ is $5770 \ years$.

A
$16989$
B
$16858$
C
$15675$
D
$17700$

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Rate of decay and Half-life

$A$ radioactive isotope decays at such a rate that after $96 \ min$,only $\frac{1}{8}$ of the original amount remains. The half-life of this nuclide in minutes is:

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Radium has an atomic weight of $226$ and a half-life of $1600$ years. The number of disintegrations produced per second from $1 \ g$ of radium is:

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The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^{9} \ s$ is $10^{10} \ s^{-1}$. The number of radioactive atoms in that sample at that instant is:

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The half-life of $_{38}^{90}Sr$ is $20 \text{ years}$. If a sample having an initial activity of $8000 \text{ dis/min}$ is taken,what would be its activity after $80 \text{ years}$?

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The unit of the decay constant for radioactive disintegration is:

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The $C^{14}$ to $C^{12}$ ratio in a wooden article is $13\%$ that of the fresh wood. Calculate the age of the wooden article. Given that the half-life of $C^{14}$ is $5770 \ years$.

Similar Questions

$A$ radioactive isotope decays at such a rate that after $96 \ min$,only $\frac{1}{8}$ of the original amount remains. The half-life of this nuclide in minutes is:

Radium has an atomic weight of $226$ and a half-life of $1600$ years. The number of disintegrations produced per second from $1 \ g$ of radium is:

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^{9} \ s$ is $10^{10} \ s^{-1}$. The number of radioactive atoms in that sample at that instant is:

The half-life of $_{38}^{90}Sr$ is $20 \text{ years}$. If a sample having an initial activity of $8000 \text{ dis/min}$ is taken,what would be its activity after $80 \text{ years}$?

The unit of the decay constant for radioactive disintegration is:

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