$A$ stationary nucleus (mass number = $A$) emits an $\alpha$-particle with velocity $v$. Find the velocity of the daughter nucleus.

The graph between the number of decayed atoms $N'$ of a radioactive element and time $t$ is:

Match List $I$ of the nuclear processes with List $II$ containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:

List $I$	List $II$
$P$. Alpha decay	$1$. ${ }_{8}^{15} O \rightarrow{ }_{7}^{15} N + \dots$
$Q$. $\beta^{+}$ decay	$2$. ${ }_{92}^{238} U \rightarrow{ }_{90}^{234} Th + \dots$
$R$. Fission	$3$. ${ }_{83}^{185} Bi \rightarrow{ }_{82}^{184} Pb + \dots$
$S$. Proton emission	$4$. ${ }_{94}^{239} Pu \rightarrow{ }_{57}^{140} La + \dots$

Codes: $P \quad Q \quad R \quad S$

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths $\lambda_N$ and $\lambda_A$ respectively. The ratio $\frac{\lambda_N}{\lambda_A}$ is closest to

Which of the alternatives gives the correct match of Column-$I$ with Column-$II$?

Column-$I$	Column-$II$
$a.$ Binding energy per nucleon for ${ }^{56} Fe$	$(i)$ $5.5 \,MeV$
$b.$ Energy of $\alpha$-particle in Geiger-Marsden experiment	$(ii)$ $200 \,MeV$
$c.$ Energy of photon of visible light	$(iii)$ $8.75 \,MeV$
$d.$ Energy released in fission of a uranium nucleus	$(iv)$ $2 \,eV$

During the disintegration of a radioactive nucleus of mass number $208$ at rest, two alpha particles each with kinetic energy $E$ are emitted. The total kinetic energy of the emitted alpha particles and the daughter nucleus after the disintegration is