The plot of the number $(N)$ of decayed atoms versus activity $(A)$ of a radioactive substance is

The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is ..........$min$

The half-life of a radioactive nucleus is $5$ years, The fraction of the original sample that would decay in $15$ years is

A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 × 10^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 ×10^9$ years (given $2^{1/3} = 1.26$)

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$

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 $....\,\Omega$