A sample of a radioactive element has a mass | vedclass

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Question

(B) The radioactive decay law is given by $m = m_0 e^{-\lambda t}$,where $m_0$ is the initial mass,$\lambda$ is the decay constant,and $t$ is the time

Vedclass · Accepted Answer

$1.35$

Vedclass · Answer

(B) The radioactive decay law is given by $m = m_0 e^{-\lambda t}$,where $m_0$ is the initial mass,$\lambda$ is the decay constant,and $t$ is the time elapsed.Given that the time elapsed is two mean lives,we have $t = 2 	au$,where $	au = \frac{1}{\lambda}$ is the mean life.Substituting $t = \frac{2}{\lambda}$ into the decay equation:$m = m_0 e^{-\lambda (2/\lambda)} = m_0 e^{-2}$.Given $m_0 = 10 \, g$ and $e \approx 2.718$,we have $e^2 \approx 7.389$.Therefore,$m = \frac{10}{7.389} \approx 1.353 \, g$.Thus,the approximate mass is $1.35 \, g$.

$A$ sample of a 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 ........ $g$.

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