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(C) The law of radioactive decay is given by the formula $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the number of nuclei remaining,

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$1/\sqrt{2}$

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(C) The law of radioactive decay is given by the formula $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the number of nuclei remaining,$N_0$ is the initial number of nuclei,$t$ is the time elapsed,and $T_{1/2}$ is the half-life.Given that the time elapsed is half of a half-life,we have $t = \frac{1}{2} T_{1/2}$.Substituting this into the decay formula:$\frac{N}{N_0} = \left( \frac{1}{2} \right)^{(T_{1/2}/2) / T_{1/2}}$$\frac{N}{N_0} = \left( \frac{1}{2} \right)^{1/2}$$\frac{N}{N_0} = \frac{1}{\sqrt{2}}$Therefore,the fraction of nuclei remaining is $1/\sqrt{2}$.

In a sample of radioactive material,what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample?

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