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.

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9$ years. Find the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9$ years (given $2^{1/3} = 1.26$).

The activity of a radioactive substance can be represented by various units. Select the correct option.

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

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)

The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.