The graph between number of decayed atoms $N'$ of a radioactive element and time $t$ is

A radioactive isotope has a half-life of $T$ years. How long will it take the activity to reduce to $(a)$ $3.125\% $ $(b)$ $1\% $ of its original value?

What is radioactivity ?

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 mean life of a radioactive material for alpha decay and beta decay are, respectively, $1620$ years and $520$ years. What is the half life of the sample (in years) ?

Define the average life of a radioactive sample and obtain its relation to decay constant and half life.