Decay constants of two radioactive samples $A$ and $B$ are $15x$ and $3x$ respectively. They have an equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $t = \frac{1}{6x}$ is

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

The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t = 0$ and $N_0/e$ counts per minute at time $t = 3 \text{ minute}$. The time (in minute) in which the activity reduces to half the value, is

The ratio of the number of active nuclei in two different samples is $2:3$. Their half-lives are $2 \ hours$ and $3 \ hours$ respectively. After $12 \ hours$,the ratio of their activities will be:

$A$ source contains two phosphorus radionuclides $_{15}^{32} P \left(T_{1/2} = 14.3 \ d\right)$ and $_{15}^{33} P \left(T_{1/2} = 25.3 \ d\right)$. Initially,$10\%$ of the decays come from $_{15}^{33} P$. How long must one wait until $90\%$ of the decays come from $_{15}^{33} P$?