Two radioactive substances $A$ and $B$ have decay constants $5\lambda $ and $\lambda $ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(\frac {1}{e})^2$ will be

Half life of radioactive element depends upon

Two radioactive substances $X$ and $Y$ originally have $N _{1}$ and $N _{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{ N _{1}}{ N _{2}}$ will be equal to

Carbon $ - 14$ decays with half-life of about $5,800\, years$. In a sample of bone, the ratio of carbon $ - 14$ to carbon $ - 12$ is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about $x$ centuries ago, where $x$ is nearest to

The half life of a radioactive sample undergoing $\alpha$ - decay is $1.4 \times 10^{17}$ s. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly

$x$ fraction of a radioactive sample decay in $t$ time. How much fraction will decay in $2t$ time