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(A) The law of radioactive decay is given by the formula: $\frac{N}{N_0} = \left( \frac{1}{2} \right)^{t/T}$,where $N$ is the remaining amount,$N_0$ i

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$2.5$

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(A) The law of radioactive decay is given by the formula: $\frac{N}{N_0} = \left( \frac{1}{2} \right)^{t/T}$,where $N$ is the remaining amount,$N_0$ is the initial amount,$t$ is the total time,and $T$ is the half-life.Given that $\frac{N}{N_0} = \frac{1}{64}$ and $t = 15$ hours.Substituting these values into the equation: $\frac{1}{64} = \left( \frac{1}{2} \right)^{15/T}$.Since $64 = 2^6$,we can write $\frac{1}{64} = \left( \frac{1}{2} \right)^6$.Equating the exponents: $\frac{15}{T} = 6$.Solving for $T$: $T = \frac{15}{6} = 2.5$ hours.

$A$ radioactive substance decays to $1/64$ of its initial value in $15$ hours. Find its half-life in hours.

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