A nucleus $_Z{X^A}$ emits $3 \alpha$ - particles and $5 \beta$ particle. The ratio of total neutrons and protons in the final nucleus is

${ }_{92}^{235} U$ atom disintegrates to ${ }_{82}^{207} Pb$ with a half-life of $10^9 yr$. In the process, it emits $7 \alpha$ particles and $n \beta^{-}$particles. Here, $n$ is

After one $\alpha $ and two $\beta $ emissions

Write nuclear reaction equations for

$(i)$ $\alpha$ -decay of $^{226}_{88} Ra$

$(ii)$ $\alpha$ -decay of $_{94}^{242} Pu$

$(iii)$ $\beta$ -decay of $_{15}^{32} P$

$(iv)$ $\beta$ -decay of $^{210}_{83}Bi$

$(v)$ $\beta^{+}$ -decay of $_{6}^{11} C$

$(vi)$ $\beta^{+}$ -decay of $_{43}^{97} Tc$

$(vii)$ Electron capture of $^{120}_{54} Xe$

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 which of the following decay, the element does not change