Question:
A sample of radioactive element has a mass of $10\, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is
A sample of radioactive element has a mass of $10\, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is
Updated On: Jun 20, 2022
- 3.70 g
- 6.30 g
- 1.35 g
- 2.50 g
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The Correct Option is C
Solution and Explanation
Mean life, $\tau=\frac{1}{\lambda}, \lambda$ being decay constant.
Also, time given $t=2 \tau=2 \times \frac{1}{\lambda}=\frac{2}{\lambda}$
Thus, mass remained after time $t$ is
$M=M_{0} e^{-\lambda t} $
$=10 e^{-\lambda \times \frac{2}{\lambda}}$
$\left(\because M_{0}=10 g\right)$
$=10 e^{-2}=\frac{10}{2}=1.35 \,g$
Also, time given $t=2 \tau=2 \times \frac{1}{\lambda}=\frac{2}{\lambda}$
Thus, mass remained after time $t$ is
$M=M_{0} e^{-\lambda t} $
$=10 e^{-\lambda \times \frac{2}{\lambda}}$
$\left(\because M_{0}=10 g\right)$
$=10 e^{-2}=\frac{10}{2}=1.35 \,g$
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