Nucleus: Composition, Size & Nuclear Force

Which of the following pair of nuclei are isobars of the element?

Four statements are given ( $A$ is mass number):

A. The volume of a nucleus is proportional to $A^{1/3}$.

B. The volume of a nucleus is proportional to $A$.

C. The difference in mass of an atom and its nucleus is called the mass defect. D. The difference in mass of a nucleus and its constituents is called the mass defect. Choose the correct answer from the options given below:

A nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$. If $\beta = 8\alpha$ then $R_{\alpha}/R_{\beta}$ is:

The ratio of the density of oxygen nucleus $\left({}_{8}^{16}\text{O}\right)$ and helium nucleus $\left({}_{2}^{4}\text{He}\right)$ is

An atom ${}_{3}^{8}X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by:

An unknown nucleus has a nuclear density of $2.29 \times 10^{17}\text{ kg/m}^{3}$ and mass of $19.926 \times 10^{-27}\text{ kg}$. Its mass number $A$ is approximately:

(Take $R_0 = 1.2 \times 10^{-15}\text{ m}, 4\pi = 12.56$)

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The density of the copper $\left({}_{29}^{64}\text{Cu}\right)$ nucleus is greater than that of the carbon $\left({}_{6}^{12}\text{C}\right)$ nucleus.

Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.

In the light of the above statements, choose the most appropriate answer from the options given below:

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______.

A nucleus has mass number $A_1$ and volume $V_1$. Another nucleus has mass number $A_2$ and Volume $V_2$. If relation between mass number is $A_2 = 4A_1$, then $\frac{V_2}{V_1} =$ __________.

From the statements given below:

(A) The angular momentum of an electron in $n$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:

The ratio of the density of oxygen nucleus (${}_{8}^{16}O$) and helium nucleus (${}_{2}^{4}\text{He}$) is

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: The nuclear density of nuclides ${}_{5}^{10}\text{B}, {}_{3}^{6}\text{Li}, {}_{26}^{56}\text{Fe}, {}_{10}^{20}\text{Ne}$ and ${}_{83}^{209}\text{Bi}$ can be arranged as $\rho_{\text{Bi}}^{\text{N}} > \rho_{\text{Fe}}^{\text{N}} > \rho_{\text{Ne}}^{\text{N}} > \rho_{\text{B}}^{\text{N}} > \rho_{\text{Li}}^{\text{N}}$

Reason R: The radius $R$ of nucleus is related to its mass number $A$ as $R = R_0 A^{1/3}$, where $R_0$ is a constant.

In the light of the above statements, choose the correct answer from the options given below

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3: 2. The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$. The value of '$x$' is :-

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1 : 2^{1/3}$. Their respective speeds have a ratio of $n : 1$. The value of $n$ is __________.

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27}$ kg and radius of nucleus is $1.5 \times 10^{-15}\,\text{A}^{1/3}$ m. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$. The value of $n$ is __________.

A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is

Which of the following figure represents the variation of $\ln\left(\frac{R}{R_0}\right)$ with $\ln A$ (if R = radius of a nucleus and A = its mass number)

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

Consider the following statements:

A. Atoms of each element emit characteristics 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 nucleus breaks into two nuclear parts, which have their velocity ratio $2 : 1$. The ratio of their nuclear radii will be

The radius R of a nucleus of mass number A can be estimated by the formula

R = (1.3 $\times$ 10–15)A1/3 m.

It follows that the mass density of a nucleus is of the order of:

(Mprot. $\cong$ Mneut $\simeq$ 1.67 $\times$ 10–27 kg)

The ratio of mass densities of nuclei of 40Ca and 16O is close to :-

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8: 27. The ratio of the radii of the nuclei (assumed to be spherical) is:

If radius of the ${}_{13}^{27}$ Al nucleus is taken to be RAl, then

the radius of ${}_{52}^{125}$Te nucleus is nearly

If the nuclear radius of 27Al is 3.6 fermi, the approximate nuclear radius of 64Cu in fermi is

Two nuclei have their mass numbers in the ratio of 1: 3. The ratio of their nuclear densities would be

If the nucleus ${}_{13}^{27}Al$ has a nuclear radius of about 3.6 fm, them ${}_{52}^{125}Te$ would have its radius approximately as

The radius of germanium (Ge) nuclide is measured to be twice the radius of ${}_{4}^{9}$Be. The number of nucleons in Ge are

Which one of the following pairs of nuclei are isotones?

If radius of the ${}_{13}^{27}Al$ nucleus is estimated to be $3.6$ fermi then the radius of ${}_{52}^{125}Te$ nucleus is estimated to be nearly

A nucleus represented by the symbol ${}_{Z}^{A}X$ has

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $2 : 1$ The ratio of their nuclear sizes will be

The mass number of a nucleus is

The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

Atomic weight of boron is $10.81$ and it has two isotopes ${}_{5}^{10}\text{B}$ and ${}_{5}^{11}\text{B}$. Then, the ratio of atoms of ${}_{5}^{10}\text{B}$ and ${}_{5}^{11}\text{B}$ in nature would be

A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to $2 : 1$. What will be the ratio of their nuclear size (nuclear radius)?

The mass number of He is 4 and that of sulphur is 32. The radius of sulphur nucleus is larger than that of helium by the factor of

The mass density of a nucleus varies with mass number $A$ as

The constituents of atomic nuclei are believed to be

In the nucleus of ${}_{11}\text{Na}^{23}$, the number of protons, neutrons and electrons are

If the nuclear force between two protons, two neutrons and between proton and neutron is denoted by $F_{pp}, F_{nn}$ and $F_{pn}$ respectively, then

The nuclei ${}_{6}\text{C}^{13}$ and ${}_{7}\text{N}^{14}$ can be described as

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

Which of the following statements is true for nuclear forces?