A sample originally contaived $10^{20}$ radioactive atoms, which emit $\alpha -$ particles. The ratio of $\alpha -$ particles emitted in the third year to that emitted during the second year is $0.3.$ How many $\alpha -$ particles were emitted in the first year?
$3\times 10^{18}$
$7\times 10^{19}$
$5\times 10^{18}$
$3\times 10^{19}$
The decay constant of a radioactive element is $0.01$ per second. Its half life period is .......$sec$
The half-life of a radioactive substance is $T$. The time taken, for disintegrating $\frac{7}{8}$ th part of its original mass will be
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
The decay constants of a radioactive substance for $\alpha $ and $\beta $ emission are ${\lambda _\alpha }$ and ${\lambda _\beta }$ respectively. If the substance emits $\alpha $ and $\beta $ simultaneously, then the average half life of the material will be
$A$ and $B$ are two radioactive substances whose half lives are $1$ and $2$ years respectively. Initially $10\, g$ of $A$ and $1\,g$ of $B$ is taken. The time (approximate) after which they will have same quantity remaining is ........... $years$