$A$ nucleus with mass number $184$ initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5\, \text{MeV}$,calculate the kinetic energy of the $\alpha$-particle in $\text{MeV}$.

Explain the conservation of linear momentum for the radioactive decay of a radium nucleus.

Explain the basic nuclear process by equation in $\beta$-decay.

List-$I$ shows different radioactive decay processes and List-$II$ provides possible emitted particles. Match each entry in List-$I$ with an appropriate entry from List-$II$, and choose the correct option.

List-$I$	List-$II$
$(P)$ ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} Pa$	$(1)$ $1 \alpha$ and $1 \beta^{+}$
$(Q)$ ${ }_{82}^{214} Pb \rightarrow{ }_{82}^{210} Pb$	$(2)$ $3 \beta^{-}$ and $1 \alpha$
$(R)$ ${ }_{81}^{210} Tl \rightarrow{ }_{82}^{206} Pb$	$(3)$ $2 \beta^{-}$ and $1 \alpha$
$(S)$ ${ }_{91}^{228} Pa \rightarrow{ }_{88}^{224} Ra$	$(4)$ $1 \alpha$ and $1 \beta^{-}$
	$(5)$ $1 \alpha$ and $2 \beta^{+}$

What does the nuclear reaction $_z{X^A} \to {_{z + 1}}{Y^A} + {_{ - 1}}{e^0} + \bar \nu$ represent?

$A$ radioactive nucleus decays as follows:
$X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4$
If the mass number and atomic number of $X_4$ are $172$ and $69$ respectively, then the atomic number and mass number of $X$ are: