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

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

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

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

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:

From the statements given below:
$(A)$ The angular momentum of an electron in $n^{\text{th}}$ orbit is an integral multiple of $\hbar$.
$(B)$ Nuclear forces do not obey inverse square law.
$(C)$ Nuclear forces are spin dependent.
$(D)$ Nuclear forces are central and charge independent.
$(E)$ Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below: