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:
$(i)\;_{88} R a^{226} \rightarrow_{86} R n^{222}+_{2} H e^{4}$
$(i i) \;^{242}_{94} Pu \rightarrow_{92}^{238} U+_{2}^{4} H e$
$(i i i)\;_{15}^{32} P \rightarrow_{16}^{32} S+e^{-}+\bar{v}$
$(i v)\;_{83}^{210} B \rightarrow_{84}^{210} P O+e^{-}+\bar{v}$
$(v)\;_{6}^{11} C \rightarrow_{5}^{11} B+e^{+}+v$
$(v i)\;_{43}^{97} T c \rightarrow_{42}^{97} M O+e^{+}+v$
$(v i i)\;_{54}^{120} X e+e^{+} \rightarrow_{53}^{120} I+v$
A radioactive nucleus undergoes a series of decay according to the scheme
$A\xrightarrow{\alpha }{{A}_{1}}\xrightarrow{\beta }{{A}_{2}}\xrightarrow{\alpha }{{A}_{3}}\xrightarrow{\gamma }{{A}_{4}}$
If the mass number and atomic number of $A$ are $180$ and $72$ respectively, then what are these number for $A_4$
In gamma ray emission from a nucleus
Assertion: ${}_Z{X^A}$ undergoes a $2\alpha -$ decays, $2\beta -$ decays and $2\gamma - $ decays and the daughter product is ${}_{Z - 2}{X^{A - 8}}$
Reason : In $\alpha - $decays the mass number decreases by $4$ and atomic number decreases by $2$. In $2\beta - $ decays the mass number remains unchanged, but atomic number increases by $1$ only.
Consider the following nuclear reactions:
$I$. ${ }_{7}^{14} N +{ }_{2}^{4} He \longrightarrow{ }_{8}^{17} O + X$
$II$. ${ }_{4}^{9} Be +{ }_{2}^{4} H \longrightarrow{ }_{6}^{12} He +Y$
Then,
If a heavy nucleus has $N / Z$ ratio higher than that required for stability, then