Properties of Nucleus - Radius, Mass, Density

Two nuclei have mass numbers in the ratio $27:125$. The ratio of their nuclear radii would be:

Two nuclei have mass numbers in the ratio $8:125$. The ratio of their nuclear radii is:

Assuming the nuclei to be spherical in shape how does the surface area of a nucleus of mass number  $A_1$  compare with that of a nucleus of mass number $A_2$ ?

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options.

Mass numbers of two nuclei are in the ratio of $4:3$. Their nuclear densities will be in the ratio of

As the mass number $A$ increases, which of the following quantities related to a nucleus do not change?

Consider the following statements $(\mathrm{X}$ and $\mathrm{Y}$ stand for two different elements$)$

$\mathrm{I}.$ $32{\mathrm{X}}^{65}$ and ${}_{33}\mathrm{Y}^{65}$ are isotopes.

$\mathrm{II}.$ $42X^{86}$ and $42Y^{85}$ are isotopes.

$\mathrm{III}.$ $85{\mathrm{X}}^{174}$ and $88{\mathrm{Y}}^{177}$ have the same number of neutrons.

$\mathrm{IV}.$ $92X^{235}$ and ${}_{94}\mathrm{Y}^{235}$ are isobars.

The correct statements are:

The triad of nuclei that is isotonic is

Imagine that a reactor converts all the given mass into energy and that it operates at a power level of ${10}^9$ watt. The mass of the fuel consumed per hour, in the reactor, will be:
(velocity of light, $c$ is $3\times {10}^{\mathrm{8 }}\mathrm{m} {\mathrm{s}}^{-1}$)

If the nucleus ${}_{13}^{27}\text{Al}$ has a nuclear radius $3.6 \mathrm{fm}$, then ${}_{32}^{125}\text{Te}$ would have its radius approximately as

Assertion : $\mathrm{C}$ and $\mathrm{Si}$ both have same lattice structure, having $4$ bonding electrons in each. However, $\mathrm{C}$ is insulator where as $\mathrm{Si}$ is intrinsic semiconductor.
Reason : The four bonding electrons in the case of $\mathrm{C}$ lie in the second orbit, whereas in the case of $\mathrm{Si}$ they lie in the third.

Two protons are separated by $10 \mathrm{\AA }$. Let $F_n$ and $F_e$ be the nuclear force and electrostatic force between them, so

A nucleus $X$ whose mass number is $36,$ is initially at rest. It is dis-integrated into $\alpha$ particle and a daughter nucleus $Y.$ If no $\gamma$-emmission is there, then chose the incorrect atternative.

Which of the following gives the correct number of protons and neutrons in a nucleus of carbon-$14 \left({}_6{}^{14}C\right)?$

Which nucleons in a nucleus are involved in
the Coulomb interaction and the strong short-range nuclear interaction?

The rest mass of a proton is $938 \mathrm{MeV} {\mathrm{c}}^{-2}$. The energy of a proton at rest is,

The nuclear radius is given by $R=r_0{A}^{1/3},$ where $r_0$ is constant and A is the atomic mass number. Then, the nuclear mass density of ${\mathrm{U}}^{238}$ is

If the radius of an atom is $1 Å,$ the total volume of a mole of these atoms will be

The ratio of the radii of the nuclei ${}_{13}\mathrm{Al}^{27}$ and ${}_{52}\mathrm{Te}^{125}$ is approximately:

A nucleus at rest splits into two nuclear parts having same density and the radii in the ratio $1 : 2.$ Their velocities are in ratio_____