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The half-life of $Ra ^{226}$ is 1620 years. Then the number of atoms decay in one second in $1 g$ of radium (Avogadro number $\left.=6.023 \times 10^{23}\right)$
The half-life of $Ra ^{226}$ is 1620 years. Then the number of atoms decay in one second in $1 g$ of radium (Avogadro number $\left.=6.023 \times 10^{23}\right)$
Updated On: May 21, 2024
- $4.23 \times 10^{9}$
- $3.16 \times 10^{10}$
- $3.61 \times 10^{10}$
- $2.16 \times 10^{10}$
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The Correct Option is C
Solution and Explanation
The number of atoms decay in one second
$\frac{d N}{d t} =\lambda N $
$=\frac{0.693}{1620 \times 365 \times 86 \times 400} \times \frac{6.023 \times 10^{23}}{226}$
$=3.61 \times 10^{10}$
$\frac{d N}{d t} =\lambda N $
$=\frac{0.693}{1620 \times 365 \times 86 \times 400} \times \frac{6.023 \times 10^{23}}{226}$
$=3.61 \times 10^{10}$
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Concepts Used:
Decay Rate
The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.
The equation for finding out the decay rate is given below:
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