Write nuclear reaction equations for:
$(i)$ $\alpha$-decay of $^{226}_{88}Ra$
$(ii)$ $\alpha$-decay of $^{242}_{94}Pu$
$(iii)$ $\beta^-$-decay of $^{32}_{15}P$
$(iv)$ $\beta^-$-decay of $^{210}_{83}Bi$
$(v)$ $\beta^+$-decay of $^{11}_{6}C$
$(vi)$ $\beta^+$-decay of $^{97}_{43}Tc$
$(vii)$ Electron capture of $^{120}_{54}Xe$

An $\alpha$-particle is a helium nucleus $(^{4}_{2}He)$. In $\alpha$-decay,the mass number decreases by $4$ and the atomic number decreases by $2$.
In $\beta^-$-decay,a neutron converts into a proton,emitting an electron $(e^-)$ and an antineutrino $(\bar{\nu})$. The atomic number increases by $1$.
In $\beta^+$-decay,a proton converts into a neutron,emitting a positron $(e^+)$ and a neutrino $(\nu)$. The atomic number decreases by $1$.
In electron capture,the nucleus captures an inner-shell electron,converting a proton into a neutron and emitting a neutrino $(\nu)$.
$(i) \; ^{226}_{88}Ra \rightarrow ^{222}_{86}Rn + ^{4}_{2}He$
$(ii) \; ^{242}_{94}Pu \rightarrow ^{238}_{92}U + ^{4}_{2}He$
$(iii) \; ^{32}_{15}P \rightarrow ^{32}_{16}S + e^- + \bar{\nu}$
$(iv) \; ^{210}_{83}Bi \rightarrow ^{210}_{84}Po + e^- + \bar{\nu}$
$(v) \; ^{11}_{6}C \rightarrow ^{11}_{5}B + e^+ + \nu$
$(vi) \; ^{97}_{43}Tc \rightarrow ^{97}_{42}Mo + e^+ + \nu$
$(vii) \; ^{120}_{54}Xe + e^- \rightarrow ^{120}_{53}I + \nu$