Radioactive nuclei that are injected into a patient collect at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiations can then be recorded by a detector. This procedure provides an important diagnostic tool called

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is ........ $x$

A radioactive nucleus (initial mass number $A$ and atomic number $Z$ emits $3 \alpha$. - particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is $5\; days$. The activity will become $5 \times 10^{-6}$ curie after $.......day$

At time $t=0$, a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition, $c$ numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$ ?

The half life of a radioactive element which has only $\frac{1}{{32}}$ of its original mass left after a lapse of $60\, days$ is ........$days$