In the uranium radioactive series,the initial nucleus is $_{92}U^{238}$ and the final nucleus is $_{82}Pb^{206}$. When the uranium nucleus decays to lead,the number of $\alpha$-particles emitted is $x$ and the number of $\beta$-particles emitted is $y$. Find $x$ and $y$.

$A$ radioactive decay forms an isotope of the original nucleus with the emission of which of the following particles?

$A$ radioactive nucleus with $Z$ protons and $N$ neutrons emits an $\alpha$-particle,$2\beta^-$-particles,and $2$ gamma rays. The number of protons and neutrons in the nucleus left after the decay,respectively,are:

In the given nuclear reaction,how many $\alpha$ and $\beta$ particles are emitted in the decay $_{92}X^{235} \to _{82}Y^{207}$?

During negative $\beta$-decay,which of the following processes occurs?

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 $\ln 10 = 2.3$]