In a sample of radioactive material,what perc | vedclass

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(B) The number of radioactive nuclei remaining undecayed after time $t$ is given by $N = N_0 e^{-\lambda t}$.The number of nuclei that have decayed af

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$63$

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(B) The number of radioactive nuclei remaining undecayed after time $t$ is given by $N = N_0 e^{-\lambda t}$.The number of nuclei that have decayed after time $t$ is $N_d = N_0 - N = N_0(1 - e^{-\lambda t})$.One mean life is defined as $	au = \frac{1}{\lambda}$.Substituting $t = 	au = \frac{1}{\lambda}$ into the decay equation:$N_d = N_0(1 - e^{-\lambda 	imes \frac{1}{\lambda}}) = N_0(1 - e^{-1}) = N_0(1 - \frac{1}{e})$.Using the value $e \approx 2.718$,we get $\frac{1}{e} \approx 0.368$.Therefore,$N_d = N_0(1 - 0.368) = N_0(0.632) = 63.2\% 	ext{ of } N_0$.Thus,approximately $63\%$ of the initial nuclei will decay during one mean life.

In a sample of radioactive material,what percentage of the initial number of active nuclei will decay during one mean life?

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