Which of the following Statements is correct?

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For ten lakh Polonium atoms, the number of disintegrations in $24$ hours is

In a radioactive decay process , the negatively charged emitted $\beta -$ particles are

If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:

$[\lambda$ is the radioactive decay constant]

The rate of disintegration was observed to be ${10^{17}}$ disintegrations per sec when its half life period is $1445$ years. The original number of particles are