In the radioactive decay of an element,it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half-life will be ...... minutes.

$A$ certain radioactive element disintegrates with a decay constant of $7.9 \times 10^{-10} / s$. At a given instant of time, if the activity of the sample is equal to $55.3 \times 10^{11}$ disintegration/second, then the number of nuclei at that instant of time is:

The half-life of $^{238}_{92}U$ undergoing $\alpha$-decay is $4.5 \times 10^{9} \text{ years}$. What is the activity of a $1 \text{ g}$ sample of $^{238}_{92}U$?

Two radioactive isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be

The atomic weight of a radioactive element is $M_w \, g/mol$. The radioactivity of $m \, g$ of its mass is: ($N_A =$ Avogadro number,$\lambda =$ decay constant)

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.