The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

The phenomenon of radioactivity is

The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1$ hour. What will be the activity after $3$ hours more?

If the radioactive decay constant of radium is $1.07 \times 10^{-4}$ per year,then its half-life period is approximately equal to ......... $years$.

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 undecayed 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 negative reciprocal of mean life time $(-\frac{1}{\tau})$.
$(D)$ Product of decay constant $(\lambda)$ and half-life time $(T_{1/2})$ is constant,equal to $\ln(2)$.
Choose the most appropriate answer from the options given below.

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is