A sample which has half life of $10^{33}$ year, if initial number of nuclei of the sample is $26 \times 10^{24}$. Then the number of nuclei decayed in $1$ year is ........... $ \times 10^{-7}$

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?

The mean life time of a radionuclide, if its activity decrease by $4\%$ for every $1h$ , would be  .......... $h$ [product is non-radioactive i.e. stable]

In a radioactive decay process, the activity is defined as $A=-\frac{\mathrm{d} N}{\mathrm{~d} t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\text {rd }}$ and $7^{\text {th }}$ half-lives, respectively, the ratio $A_1 / A_2$ is. . . . . . .

$\beta$- rays emitted by a radioactive material are

The average life $T$ and the decay constant $\lambda $ of a radioactive nucleus are related as