The radioactive nucleus $_7N^{13}$ decays to $_6C^{13}$ through the emission of

The nucleus produced due to $\alpha$-decay of the nucleus $_Z{X^A}$ is

When a radioactive isotope ${}_{88}^{228}Ra$ decays in series by the emission of $3$ alpha particles and $1$ beta particle,the isotope finally formed is

After the decay of a single $\beta$ particle, the parent and daughter nuclei are

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 $\ln 10 = 2.3$]

$A$ radioactive nuclide of element $X$ decays to form element $Y$. The graph representing the rate of production of $Y$ in a sample of $X$ is: