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

$A$ nucleus with mass number $184$ initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5\, \text{MeV}$,calculate the kinetic energy of the $\alpha$-particle in $\text{MeV}$.

In the nuclear reaction ${}_{92}^{235}U$ decaying to ${}_{91}^{231}Pa$,what are the particles emitted?

In a radioactive sample,${ }_{19}^{40} K$ nuclei decay into stable ${ }_{20}^{40} Ca$ nuclei with a decay constant of $4.5 \times 10^{-10} \text{ per year}$ or into stable ${ }_{18}^{40} Ar$ nuclei with a decay constant of $0.5 \times 10^{-10} \text{ per year}$. Given that in this sample,all the stable ${ }_{20}^{40} Ca$ and ${ }_{18}^{40} Ar$ nuclei are produced by the ${ }_{19}^{40} K$ nuclei only. In time $t \times 10^9 \text{ years}$,if the ratio of the sum of stable ${ }_{20}^{40} Ca$ and ${ }_{18}^{40} Ar$ nuclei to the radioactive ${ }_{19}^{40} K$ nuclei is $99$,the value of $t$ will be: [Given $\ln 10 = 2.3$]

$A$ nucleus of an element ${}_{84}X^{202}$ emits an $\alpha$-particle first,a $\beta$-particle next,and then a gamma photon. The final nucleus formed has an atomic number:

$A$ radioactive element ${}_{92}^{242}X$ emits two $\alpha$-particles,one electron,and two positrons. The product nucleus is represented by ${}_{P}^{234}Y$. The value of $P$ is $..................$