The relation between half-life $(T)$ and decay constant $(\lambda)$ is

In a nuclear reactor,the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50 \text{ minutes}$,then in the steady power generation,the number of radionuclides is:

$A$ sample originally contained $10^{20}$ 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?

In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

If $10\%$ of a radioactive material decays in $5\, days$,then the amount of the original material left after $20\, days$ is approximately .......... $\%$

The half-life of radium is $1600 \, \text{years}$. The fraction of the radium sample that will remain after $6400 \, \text{years}$ is: