Which of the following can penetrate through an aluminum sheet of $20 \, cm$ thickness?

$A$ nuclear reaction is given by ${}_{Z}X^{A} \to {}_{Z+1}Y^{A} + {}_{-1}e^{0} + \bar{\nu}$,which represents:

$_{86}A^{222} \to _{84}B^{210}$. In this reaction,how many $\alpha$ and $\beta$ particles are emitted?

If a heavy nucleus has an $N/Z$ ratio higher than that required for stability,then:

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 ${ }_{Z} X^{A}$ emits an $\alpha$-particle with velocity $v$. The recoil speed of the daughter nucleus is