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

A radioactive substance has a half-life of $1$ year. The fraction of this material, that would remain after $5$ years will be

The particle that possesses half integral spin as

A radioactive sample has an average life of $30\, {ms}$ and is decaying. A capacitor of capacitance $200\, \mu\, {F}$ is first charged and later connected with resistor $^{\prime}{R}^{\prime}$. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of $^{\prime}R^{\prime}$ should be $….\,\Omega$

The half life of a radioactive substance against $\alpha  – $ decay is $1.2 \times 10^7\, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance