Nucleus was discovered in

The distance of the closest approach of an $\mathrm{\alpha }-$particle reaching a nucleus with momentum $\text{'}\mathrm{p}\text{'}$ is ${\mathrm{r}}_0$. When the $\mathrm{\alpha }-$ particle travels towards the same nucleus with momentum $\frac{\mathrm{P}}{2}$, the distance of the closest approach will be:

Initial mass of ${}_{84}{\mathrm{Po}}^{218}$ is $1$ gram. After what time $0.875$ gram of it will be disintegrated? $\left({\mathrm{T}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=3 \mathrm{minutes}\right)$

Consider the following statements $(\mathrm{X}$ and $\mathrm{Y}$ stand for two different elements$)$

$\mathrm{I}.$ $32{\mathrm{X}}^{65}$ and ${}_{33}\mathrm{Y}^{65}$ are isotopes.

$\mathrm{II}.$ $42X^{86}$ and $42Y^{85}$ are isotopes.

$\mathrm{III}.$ $85{\mathrm{X}}^{174}$ and $88{\mathrm{Y}}^{177}$ have the same number of neutrons.

$\mathrm{IV}.$ $92X^{235}$ and ${}_{94}\mathrm{Y}^{235}$ are isobars.

The correct statements are:

Consider the nuclei of ${}^{27}\mathrm{Al}$ and ${}^{64}\mathrm{Cu}$. Which of the following statements is correct?