$A$ nucleus of mass $218\, amu$ in a free state decays to emit an $\alpha$-particle. The kinetic energy of the emitted $\alpha$-particle is $6.7\, MeV$. The recoil energy (in $MeV$) of the daughter nucleus is:

When a nucleus with atomic number $Z$ and mass number $A$ undergoes a radioactive decay process:

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

$1 \text{ Curie}$ is equal to

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 $\ln 10 = 2.3$]

The end product of the decay of $ { }_{90} Th^{232} $ is $ { }_{82} Pb^{208} $. The number of $ \alpha $ and $ \beta $ particles emitted are respectively: