In a fossil bone,the ratio of $^{14}C : ^{12}C$ is $1/16$ of the ratio found in a living animal. If the half-life of $^{14}C$ is $5730 \text{ years}$,find the age of the fossil bone in years.

The activity of a radioactive sample falls from $700 \; s^{-1}$ to $500 \; s^{-1}$ in $30 \; min$. Its half-life is close to ......... $min$.

$C^{14}$ has a half-life of $5700$ years. At the end of $11400$ years,the actual amount left is:

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6\%$ of the time it decays by $\alpha$-decay and $33.3\%$ of the time it decays by $\beta$-decay. If the effective half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay? (in years)

$A$ radioactive element decays to form a stable nuclide. The rate of decay of the reactant $\left( \frac{dN}{dt} \right)$ will vary with time $(t)$ as shown in which figure?

The phenomenon of radioactivity is