The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is

$A$ nucleus with mass number $220$ initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5\, MeV$,calculate the kinetic energy of the $\alpha$-particle in $MeV$.

Which of the following nuclear reactions is possible?

$A$ nucleus $X$ undergoes the following transformation:
$X \xrightarrow{\alpha} Y$
$Y \xrightarrow{2\beta} Z$
Then:

Radioactive nuclei that are injected into a patient collect at certain sites within their 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:

In a radioactive decay chain,the initial nucleus is ${}_{90}^{232}Th$. At the end,$6$ $\alpha$-particles and $4$ $\beta$-particles are emitted. If the final nucleus is ${}_{Z}^{A}X$,then $A$ and $Z$ are given by: