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

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

Certain radioactive substance reduces to $25\%$ of its value in $16\ days$. Its half-life is .......... $days$

At some instant, a radioactive sample $S_1$ having an activity $5\,\mu Ci$  has twice the number of nuclei as another sample $S_2$  which has an activity of  $10\,\mu Ci.$  The halflives of $S_1$  and  $S_2$ are

The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of $30\, minutes$ decreases to $5\,{s^{ - 1}}$ after $2\, hours.$ The initial count rate was..........${s^{ - 1}}$

The half life of radium is $1620$ years and its atomic weight is $226\, k\,gm$ per kilomol. The number of atoms that will decay from its $1\, gm$ sample per second will be

(Avogadro's number $N = 6.02 \times {10^{26}}$atom/kilomol)