Consider the following statements:
$A.$ Atoms of each element emit a characteristic spectrum.
$B.$ According to Bohr's postulate, an electron in a hydrogen atom revolves in a certain stationary orbit.
$C.$ The density of nuclear matter depends on the size of the nucleus.
$D.$ A free neutron is stable, but a free proton decay is possible.
$E.$ Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below:

  • A
    $A, B$ and $E$ only
  • B
    $B$ and $D$ only
  • C
    $A, C$ and $E$ only
  • D
    $A, B, C, D$ and $E$

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

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

$A$ radioactive nucleus emits an $\alpha$-particle to become a stable nucleus. If the velocity of the $\alpha$-particle is $\upsilon$ and the mass number of the original radioactive nucleus is $A$,what will be the velocity of the daughter nucleus?

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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$(iv)$ $2 \,eV$

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