After the decay of a single $\beta$ particle,the parent and daughter nuclei are

How many alpha and beta particles are emitted when Uranium ${}_{92}U^{238}$ decays to lead ${}_{82}Pb^{206}$?

Find the $Q$-value and the kinetic energy of the emitted $\alpha$-particle in the $\alpha$-decay of $(a) \; ^{226}_{88} Ra$ and $(b) \; ^{220}_{86} Rn$.
Given:
$m(^{226}_{88} Ra) = 226.02540 \; u$
$m(^{222}_{86} Rn) = 222.01750 \; u$
$m(^{220}_{86} Rn) = 220.01137 \; u$
$m(^{216}_{84} Po) = 216.00189 \; u$
$m(^{4}_{2} He) = 4.002603 \; u$

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 $2 \beta^{+}$

$A$ radioactive nucleus emits $4 \alpha$ particles and $7 \beta$ particles in succession. The ratio of the number of neutrons to that of protons in the final nucleus is $[A = \text{mass number}, Z = \text{atomic number}]$

Which spectrum is continuous?