Plutonium decays with a half-life of $24000 \,years$. If the plutonium is stored for $72000 \,years$, then the fraction of plutonium that remains is

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life .......... $\%$

A radioactive sample is $\alpha$-emitter with half life $138.6$ days is observed by a student to have $2000$ disintegration/sec. The number of radioactive nuclei for given activity are

Following statements related to radioactivity are given below

$(A)$ Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

$(B)$ The number of un-decayed nuclei in the radioactive sample decays exponentially with time.

$(C)$ Slope of the graph of $\log _{e}$ (no. of undecayed nuclei) $Vs$. time represents the reciprocal of mean life time $(\tau)$.

$(D)$ Product of decay constant ( $\lambda$ ) and half-life time $\left(T_{1 / 2}\right)$ is not constant.

Choose the most appropriate answer from the options given below

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half its value is 

The half life of $^{131}I$ is $8\, days$. Given a sample of $^{131}I$ at time $t = 0,$ we can assert that