The rate of disintegration was observed to be | vedclass

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(B) The rate of disintegration is given by $\frac{dN}{dt} = \lambda N_0 = 10^{17} \, s^{-1}$.The half-life $T_{1/2} = 1445 \, 	ext{years}$.Convert th

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$6.6 	imes 10^{27}$

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(B) The rate of disintegration is given by $\frac{dN}{dt} = \lambda N_0 = 10^{17} \, s^{-1}$.The half-life $T_{1/2} = 1445 \, 	ext{years}$.Convert the half-life into seconds: $T_{1/2} = 1445 	imes 365 	imes 24 	imes 3600 \approx 4.55 	imes 10^{10} \, s$.The decay constant $\lambda$ is given by $\lambda = \frac{0.693}{T_{1/2}} = \frac{0.693}{4.55 	imes 10^{10}} \approx 1.52 	imes 10^{-11} \, s^{-1}$.Using the relation $\frac{dN}{dt} = \lambda N_0$,we find the original number of particles $N_0$:$N_0 = \frac{dN/dt}{\lambda} = \frac{10^{17}}{1.52 	imes 10^{-11}} \approx 6.58 	imes 10^{27} \approx 6.6 	imes 10^{27}$.

The rate of disintegration was observed to be $10^{17}$ disintegrations per second when its half-life period is $1445$ years. The original number of particles is:

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