If one starts with one curie of radioactive substance ($T_{1/2}  = 12\,hrs$) the activity left after a period of $1$ week will be about

A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 × 10^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 ×10^9$ years (given $2^{1/3} = 1.26$)

How much mass of uranium to be destroyed per minute to operate a nuclear reactor of $600\,MW$

At $t = 0$, number of active nuclei in a sample is $N_0$. How much no. of nuclei will decay in time between its first mean life and second half life?

If the mass of a radioactive sample is doubled, the activity of the sample and the disintegration constant of the sample are respectively

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$