The decay constant of the end product of a radioactive series is

An artificial radioactive decay series begins with unstable $_{94}^{241}Pu$. The stable nuclide obtained after eight $\alpha$-decays and five $\beta$-decays is

Assertion: ${}_{Z}{X^{A}}$ undergoes $2\alpha$-decays,$2\beta$-decays,and $2\gamma$-decays,and the daughter product is ${}_{Z-2}{X^{A-8}}$.
Reason: In $\alpha$-decays,the mass number decreases by $4$ and the atomic number decreases by $2$. In $\beta$-decays,the mass number remains unchanged,but the atomic number increases by $1$.

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

$A$ radioactive nucleus decays as follows:
$X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4$
If the atomic number and the mass number of $X$ are $72$ and $180$ respectively,then the mass number and atomic number of $X_4$ are:

For the radioactive nuclei that undergo either $\alpha$ or $\beta$ decay, which one of the following cannot occur?