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 $^{120}_{54} Xe$

$\alpha$ is a nucleus of helium $\left(_{2} H e^{4}\right)$ and $\beta$ is an electron $(e^{-}$ for $\beta^{-}$ and $e^{+}$ for $\beta^{+}$) In every $\alpha$ decay, there is a loss of $2$ protons and $2$ neutrons. In every $\beta^{+}$ -decay, there is a loss of $1$ proton and a neutrino is emitted from the nucleus. In every $\beta^{-}$ -decay, there is a gain of $1$ proton and an antineutrino is emitted from the nucleus. For the given cases, the various nuclear reactions can be written as:

$(i)\;_{88} R a^{226} \rightarrow_{86} R n^{222}+_{2} H e^{4}$

$(i i) \;^{242}_{94} Pu \rightarrow_{92}^{238} U+_{2}^{4} H e$

$(i i i)\;_{15}^{32} P \rightarrow_{16}^{32} S+e^{-}+\bar{v}$

$(i v)\;_{83}^{210} B \rightarrow_{84}^{210} P O+e^{-}+\bar{v}$

$(v)\;_{6}^{11} C \rightarrow_{5}^{11} B+e^{+}+v$

$(v i)\;_{43}^{97} T c \rightarrow_{42}^{97} M O+e^{+}+v$

$(v i i)\;_{54}^{120} X e+e^{+} \rightarrow_{53}^{120} I+v$