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The nuclear force - class-VIII

Description: the nuclear force
Number of Questions: 38
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Tags: atomic nuclei inside the atom atomic, nuclear and particle physics nuclei chemistry physics
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The angular momentum of electrons in an atom produces:

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. light

  2. nuclear fission

  3. magnetic moment

  4. zeeman effect

Show answer
Correct Option: A

The binding energy per nucleon for $\mathrm { U } ^ { 238 }$ about 7.5Mev where as it is about 8.5 Mev for a nucleus having a mass half of Uranium. If $\mathrm { U } ^ { 238 }$ splits into two exact halves the energy released would be

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. 6.4 Mev

  2. 119 Mev

  3. 238 Mev

  4. 476 Mev

Show answer
Correct Option: C

The excitation energy of a hydrogen like ion to first excited state is 40.8 eV. The energy needed to remove the electron from the ion the ground state is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. 54.4 eV

  2. 62.6 eV

  3. 72.6 eV

  4. 58.6 eV.

Show answer
Correct Option: A
Explanation:

For a hydrogen atom like system the energy for $n^{th}  $ level is given by $E _n=\dfrac{-13.6Z^2}{n^2}eV$

So the ground state energy will be $E _1=\dfrac{-13.6Z^2}{1}eV$
and for the state $n=2$ the energy is $E _2=\dfrac{-13.6Z^2}{4}eV$
So the excitation energy foe this state will be $E _2 -E _1=10.2Z^2eV$
as it is given to be $40.8eV$  so $Z^2=4$ or $Z=2$
So the energy in ground state will be $E _1=-54.4eV$
so the inonization energy will be $-(-54.4eV)=54.4eV$

What is the maximum value of binding energy per nucleon ?

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. 8 MeV

  2. 8.8 MeV

  3. 7.6 MeV

  4. 1.1 MeV

Show answer
Correct Option: B
Explanation:

Answer is (B)

The Binding energy curve reaches a maximum value of 8.79

Identify the correct statement/statements:
a) At greater distances nuclear forces are negligible
b) Nuclear forces are non central forces
c) Nuclear forces are weakest in nature
d) Nuclear forces are charge dependent forces

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. a, b

  2. b, c

  3. c, d

  4. a, d

Show answer
Correct Option: A
Explanation:

Nuclear forces properties :
1) They will act upto nearly one ferms. Beyond that they become negligible.
2) Charge independent : $F _{pp} = F _{pn} = F _{nn}$
3) They do not act along the line joining the centres of the nuclears, so they are non-central forces.
4) Nuclear forces are strong in nature.
So, correct choice is option A.

Let $F _{pp},F _{pn}$ and $F _{nn}$ denote the magnitudes of the nuclear force by a proton on a proton, by a proton on a neutron and by a neutron on a neutron respectively when the separation is less than one Fermi. Then

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _{pp}>F _{pn}= F _{nn}$

  2. $F _{pp}=F _{pn}= F _{nn}$

  3. $F _{pp}>F _{pn}> F _{nn}$

  4. $F _{pp}< F _{pn}= F _{nn}$

Show answer
Correct Option: B
Explanation:

At separation less than one fermi,  the nuclear force of attraction is strongly active and Nuclear force is charge independent force.

Hence , $F _{pp} = F _{pn} = F _{nn}$

Among the following, short range, charge independent and spin dependent forces are

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Gravitational forces

  2. Nuclear forces

  3. Electromagnetic forces

  4. Weak forces

Show answer
Correct Option: B
Explanation:

Nuclear force is short range, charge independent and spin independent force.

Among gravitational,electrostatic and nuclear forces,the two attractive forces between two neutrons are

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Electrostatic and nuclear

  2. Electrostatic and gravitational

  3. Gravitational and nuclear

  4. Electrostatic

Show answer
Correct Option: C
Explanation:

Neutrons have no charge on them. So, there is no electrostatic force. But we have gravitational and nuclear forces on two neutrons because neutrons have masses and gravitational force depends on mass.
So, correct choice is option C.

Among the following interactions, the one of least significance in nuclear physics is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. nuclear interaction

  2. gravitational interaction

  3. electrostatic interaction

  4. electromagnetic interaction

Show answer
Correct Option: B
Explanation:

Since, masses of electrons, protons and neutrons are negligible. So, we often neglect gravitational interaction in nuclear physics.

Two protons attract each other when the distance between them is 

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $10^{-18}$m

  2. $10^{-20}$m

  3. $10^{-15}$m

  4. $10^{-22}$m

Show answer
Correct Option: C
Explanation:

Two protons attracts each other when distance between them is less than $10^{-15}m.$

Two protons are kept at a separation of $10$nm. Let $F _{n}$ be the nuclear force and $F _{e}$ be electromagnetic force between them. Then,

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _{e}= F _{n}$

  2. $F _{e}>> F _{n}$

  3. $F _{e}<< F _{n}$

  4. $F _{n}= F _{e}$

Show answer
Correct Option: B
Explanation:

At separation greater than fermi, nuclear force is negligible. So, electromagnetic force is much powerful than nuclear force.
So, correct chioce is option B.

Attractive Force exists between two protons inside the Nucleus. This is due to :

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Gravitational Forces

  2. Electro magnetic Forces

  3. Weak Nuclear Forces

  4. Strong Nuclear Forces

Show answer
Correct Option: D
Explanation:

The forces that bind fermions (electron, proton, neutron) together are termed as weak forces. Whereas the forces that bind the constituents of a nucleus are strong nuclear force.

Repulsive forces exists between two protons outside the nucleus. This is due to

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Gravitiaonal Forces

  2. Electro magnetic Forces

  3. Weak Nuclear Forces

  4. Strong Nuclear Forces

Show answer
Correct Option: B
Explanation:

Electromagnetic force.

This force is described by electromagnetic fields, and has innumerable physical instances including the interaction of electrically charged particles and the interaction of uncharged magnetic force fields with electrical conductors.

The kind(s) of force that is/are present between two protons in a nucleus is/are _______.

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Electrostatic force

  2. Nuclear force

  3. Magnetic force

  4. Both (A) and (B)

Show answer
Correct Option: D
Explanation:
Two protons are subject to two forces;- the nuclear force and the electrostatic force. When they are very close together the nuclear force is dominant, and when they are far apart electrostatic force is dominant
Hence two kinds of forces present between two protons in a nucleus.
However magnitude of Nuclear force is much more than Electrostatic force

A free hydrogen atom in ground state is at rest. A neutron of kinetic energy K collides with the hydrogen atom. After collision hydrogen atom emits two photons in succession one of which has energy $2.55eV$. Assume that the hydrogen atom and neutron has same mas. 

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Minimum value of K is $25.5eV$

  2. Minimum value of K is $12.75eV$

  3. The other photon has energy $10.2eV$

  4. Th upper energy level is of excitation energy $12.5eV$

Show answer
Correct Option: A

Which  of the following statement is incorrect for nuclear forces ?

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. These are strongest in magnitude

  2. They are charge dependent

  3. They are effective only for short ranges

  4. They result for interaction of every nucleon with the nearest limited number of nucleons

Show answer
Correct Option: B
Explanation:

As we know that nucleus force is a strong force , they are strongest in magnitude. They are short range because the distance between the nucleon $0.7$ fermi which is very small.
They are charged independent. They result for interaction of every nucleon with the nearest limited number of nucleons.

The bin ding energy of deuteron $ (^2 _1H) $ is 1.15 MeV per nucleon and an alpha particle $ ( ^4 _2He ) $ has binding energy of 7.1 MeV per nucleon . then in the reaction $^2 _1H + ^2 _1H \rightarrow ^4 _2He + Q $ the energy Q is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. 33.0 MeV

  2. 28.4 MeV

  3. 23.8 MeV

  4. 4.6 MeV

Show answer
Correct Option: C

A neutron exerts a force on a proton which is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. gravitational

  2. electromagnetic

  3. nuclear

  4. weak

Show answer
Correct Option: A,C
Explanation:

Nuclear force
The nuclear force (or nucleon interaction or residual strong force) is the force of protons and neutrons, subatomic particles that are collectively called nucleons. The nuclear force is responsible for binding protons and neutrons into atomic nuclei. Neutrons and protons are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience a Coulomb repulsion that tends to push them apart, but at short range, the nuclear force is sufficiently attractive as to overcome the electromagnetic repulsive force. The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons which form it.
Gravitational force
This force acts b.w two particles having non zero mass
Electromagnetic force
Electromagnetism is the study of the electromagnetic force which is a type of physical interaction that occurs between electrically charged particles. 

Since neutron is uncharged, the electromagnetic force is zero.

A proton exerts a force on a proton which is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. gravitational

  2. electromagnetic

  3. nuclear

  4. weak

Show answer
Correct Option: A,B,C
Explanation:

Nuclear force
The nuclear force (or nucleon interaction or residual strong force) is the force of protons and neutrons, subatomic particles that are collectively called nucleons. The nuclear force is responsible for binding protons and neutrons into atomic nuclei. Neutrons and protons are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience a Coulomb repulsion that tends to push them apart, but at short range the nuclear force is sufficiently attractive as to overcome the electromagnetic repulsive force. The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons which form it.
Gravitational force
This force acts b.w two particles having non zero mass
Electromagnetic force
Electromagnetism is the study of the electromagnetic force which is a type of physical interaction that occurs between electrically charged particles.

At a specific instant emission of radioactive compound deflected in a magnetic field. The compound can emit 

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Electrons

  2. Protons

  3. $He^{2+}$

  4. All of these

Show answer
Correct Option: D
Explanation:

Electrons, protons and helium ions are deflected in the magnetic field.

So, the compound can emit electrons protons and $H{e^{2 + }}$.
Hence, Option $A,B,C$ are correct.
so the final answer is D.

Identify the wrong statement in the following Coulomb's law correctly describes the electric force that

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. binds the electrons of an atom to its nucleus.

  2. binds protons and neutrons in the nucleus of an atom.

  3. binds atoms together to form molecules.

  4. binds atoms and molecules to form solids.

Show answer
Correct Option: B
Explanation:

Answer is (B).

As the Coloumb's force applies between two charged bodies and the neutron doesn't have charge.

Protons are placed in a magnetic field in a $Z$ direction (magnitude = 2.3 T). The energy difference between a state with $Z$ component of proton spin angular momentum parallel to the field and antiparallel to the field is 

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $4.05\times10^{7} eV$

  2. $4.05\times10^{-7} eV$

  3. $2.025\times10^{7} eV$

  4. $2.025\times10^{-7} eV$

Show answer
Correct Option: B
Explanation:

$U _{1}$ = $|S _{z}|$ $B$
=$-2.7928\times(2.3T)\times 3.152\times10^{-8}\left(\displaystyle\ \frac{eV}{T} \right)$
= $-2.025\times10^{-7} eV$ (When $B$ and $|S _{z}|$ are parallel
$U _{2}$ = $+2.025\times10^{-7} eV$ when $B$ and $|S _{z}|$ are antiparallel.
$\therefore$ $\triangle U$ = $U _{2}$ -$U _{1}$ = $4.05\times10^{-7} eV$

Two Nucleons are at a separation of $1$ fermi. Proton have a charge $1.6\times10^{-19}$ $C$, the nuclear force between them is $F _{1}$ both are neutrons, $F _{2}$ if both are protons, $F _{3}$ if one neutron and one proton then

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _{1}$ = $F _{2}$>$F _{3}$

  2. $F _{1}$ = $F _{2}$ = $F _{3}$

  3. $F _{1}$<$F _{2}$<$F _{3}$

  4. $F _{1}$ = $F _{2}$<$F _{3}$

Show answer
Correct Option: B
Explanation:

Nuclear force is independent of charge of the nucleons.

Thus nuclear force is same for any pair of two nucleons which are at same distance apart.
$\therefore        F _1 = F _2 = F _3$

Nuclear force exist between

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Proton - Proton

  2. Proton - Neutron

  3. Neutron - Neutron

  4. All of the above

Show answer
Correct Option: D
Explanation:

All of the above.

Nuclear force exist between
Proton- Proton
Proton- Neutron
Neutron- Neutron
As Neutrons and Protons both are nucleons

Two nucleons are at a separation of $1$ fermi. The net force between them is $F _{1}$, if both are neutrons, $F _{2}$ if both are protons and $F _{3}$, if one is a proton and the other is a neutron

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _{1} > F _{2} > F _{3}$

  2. $F _{2} > F _{1} > F _{3}$

  3. $F _{1} = F _{3} > F _{2}$

  4. $F _{1} = F _{2} > F _{3}$

Show answer
Correct Option: C
Explanation:

Nuclear forces are the strongest forces in nature.
Nuclear forces are the strong forces of attraction which hold together the nucleons (neutrons and protons) in the tiny nucleus of an atom, inspite of strong electrostatic forces of repulsion between protons. Nuclear forces act between a pair of neutrons, a pair of protons and also between a neutron, proton pair with the same strength. This shows that nuclear forces are independent of charge.
The attractive nuclear force is the same for any pair of nucleons. Thus, $F _{1} = F _{3}$ when there are no electrostatic forces, but
$F _{2} =$ attractive nuclear force $-$ repulsive electrostatic force
Hence, $F _{1} = F _{3} > F _{2}$

Two nucleons are at a separation of one Fermi. Protons have a charge of $+1.6\times 10^{-19}$ C. The net nuclear force between them is $F _1$, if both are neutrons, $F _2$ if both are protons and $F _3$ if one is proton and the other is neutron. Then.

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _1 = F _2 >F _3$

  2. $F _1=F _2=F _3$

  3. $F _1< F _2 < F _3$

  4. $F _1 > F _2 > F _3$

Show answer
Correct Option: B
Explanation:
Mass of proton = Mass of neutron = $1.67\times 10^{-27}Kg$
So, force between proton - proton, proton - neutron, neutron - neutron are equal.
So, $F _1=F _2=F _3$

A radioactive nucleus has specific binding energy '${E} _{1}$'. It emits an $\alpha$-particle. The resulting nucleus has specific binding energy '${E} _{2}$'. Then

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. ${E} _{2}={E} _{1}$

  2. ${E} _{2}<{E} _{1}$

  3. ${E} _{2}>{E} _{1}$

  4. ${E} _{2}=0$

Show answer
Correct Option: C
Explanation:

A radioactive nucleus always decays into more stable nucleus and high binding energy corresponds to more stable nucleus. Therefore, after emitting an alpha particle energy $E _2$ will be more than the initial energy $E _1$.

The nature of the electrostatic force and nuclear force between a proton and a neutron inside a nucleus are respectively.

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Repulsive and attractive

  2. Zero and attractive

  3. Repulsion and repulsive

  4. Attractive and attractive

Show answer
Correct Option: B
Explanation:

Since neutron is neutral in nature, the electrostatic force between neutron and proton is zero. They have attractive nuclear force between them which causes the nucleus to bind together. 

Range of nuclear force is approximately

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $2 \times 10^{-l5} m$

  2. $1.5 \times 10^{-20} m$

  3. $7.2 \times 10^{-4} m$

  4. $1.4 \times 10^{-15} m$

Show answer
Correct Option: A
Explanation:
The nuclear force is powerfully attractive between nucleons at distance of about 1 femtometre or $1.0\times{10}^{-15}$ metre, but it rapidly decreases to insignificance at distance beyond about 2.5fm
So, $(A)$ is correct.

Which of the following statements is wrong

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Strong nuclear forces are the strongest forces

  2. Nuclear forces are very short range forces

  3. nuclear force increases when the number of nucleons is increased

  4. None of these

Show answer
Correct Option: D
Explanation:
There are four fundamental interactions account for all observed forces. These interactions are strong nuclear, electromagnetic, weak nuclear and gravitational
The strongest of these four is the strong nuclear. It is responsible for binding together the fundamental particles of matter to form larger particles.
However this interaction operates at a very short range inside the nucleus (as little as $1$fm- $1$ femo meter or ${ 10 }^{ -15 }$ meter)
Nuclear force is defined as the force exerted between numbers of nucleons. So nuclear force increases when the number of nucleons is increased. All statements are correct.

The force between protons in the nucleus will b

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. only nuclear

  2. only coulomb

  3. nuclear & coulomb

  4. coulomb & gravitational

Show answer
Correct Option: C
Explanation:
The electrostatic force between an electron and a proton is given by Coulombs Law of force, that is directly proportional; to the product of charges of electron and the proton and inversely proportional to the square of distance between the two particles
Another force on proton is nuclear force as it the force exerted between numbers of nucleons. This force is attractive in nature which binds protons and neutrons in the nucleus together.

If the ionization energy of hydrogen atom is $13.6 eV$ then the wavelength of the radiation required to excite the electron in $L{ i }^{ ++ }$ from first to third Bohr orbit is approximately

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $1140 A$

  2. $914 A$

  3. $11.4 A$

  4. $134 A$

Show answer
Correct Option: B
Explanation:

Ionisation energy is given by

$E = 13.6\ eV$ (given)
or $E = 13.6 \times 1.6 \times 10^{-19} J ....(1)$
also $E = hv$
$E = \dfrac{hc}{\lambda} ....(2)$
equation $(1)$ and $(2)$
$\dfrac{hc}{\lambda} = 13.6 \times 1.6 \times 10^{-19}$
$\lambda = \dfrac{h \times c}{13.6 \times 1.6 \times 10^{-19}}$
$\lambda = \dfrac{3 \times 10^{8} \times 6.63 \times 10^{-34}}{13.6 \times 1.6 \times 10^{-19}}$
$\lambda = 914 \times 10^{-10} m$
$\lambda = 914 A^o$

Range of weak nuclear force is

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $10^{16}$ m

  2. $10^{10}$ m

  3. $10^{-12}$ m

  4. $10^{-18}$ m

Show answer
Correct Option: D

Mass numbers of the elements A, B, C and D are 30, 60, 90 and 120 respectively. the  specific binding energy of them are 5 MeV, 8.5 MeV, 8 MeV and 7 MeV respectively. then, in which of the following reaction/s energy is released?
(1) $ D \rightarrow 2B $
(2) $ C \rightarrow B+A $
(3) $ B \rightarrow 2A $

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. only in (1)

  2. in(2), (3)

  3. in (1), (3)

  4. in (1), (2) and (3)

Show answer
Correct Option: A

If $F _{NN}$, $F _{NP}$, $F _{PP}$ denotes net force between neutron and neutron, neutron and proton, proton and proton then

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $F _{NN}$ = $F _{NP}$ = $F _{PP}$

  2. $F _{NN}$ = $F _{NP}$ > $F _{PP}$

  3. $F _{NN}$ = $F _{NP}$ < $F _{PP}$

  4. $F _{NN}$ >$F _{NP}$>$F _{PP}$

Show answer
Correct Option: A
Explanation:

At separation less than one fermi, hence nuclear force of attraction is strongly active.
Nuclear force is charge independent force.
So, $F _{pp} = F _{pn} = F _{nn}$

Consider an $\alpha$-particle just in contact with a $ _{\;  92}^{238}\textrm{U}$ nucleus. The Coulombic repulsion energy  (i.e, the height of the Coulombic barrier between $^{238}\textrm{U}$ and alpha particle) assuming that the distance between them is equal to the sum of their radii is 

chemistry nuclei nuclear force the nuclear force nuclear force and binding energy

  1. $16.35 \, MeV$

  2. $46.66 \, MeV$

  3. $22.24 \, MeV$

  4. $26.14 \, MeV$

Show answer
Correct Option: D
Explanation:

The expression for the radius of the nucleus is as shown below.
$r _{nucleus} =1.3\times 10^{-13}(A)^{1/3}$; where $A$ is mass number
Radius of  $ _{92}^{238}\textrm{U}=1.3\times10^{-13}\times (238)^{1/3}$
                           $= 8.06\times 10^{-13}cm$
Radius of $ _{2}^{4}\textrm{He}=1.3\times10^{-13}\times (4)^{1/3}$
                         $=2.06\times10^{-13}cm$
Total distance between uranium and helium nuclei is equal to the sum of their radii. 

It is $=(8.06 + 2.06)\times10^{-13}=10.12\times10^{-13}cm$ 

The Coulombic repulsion energy is: 
$\displaystyle \frac{Q _1Q _2}{r}$ $\displaystyle =\frac{92\times 4.8\times 10^{-10}\times 2\times 4.8\times 10^{-10}}{10.12\times 10^{-13}}erg$                (because $Q _1$ and  $Q _2$  in  esu and r in cm)     
                                      
            $=418.9\times 10^{-7}erg= 418.9\times 10^{-14}$J

            $=418.9\times 10^{-14}/1.602\times 10^{-19}\ eV$
              
            $\displaystyle =\frac{26.14\times 10^6}{10^6}\ MeV$

            $=26.14 \, MeV$

Hence, the coulombic repulsion energy is $26.14\ MeV$.

A hydrogen atom having kinetic energy $E$ collides with a stationary hydrogen atom. Assume all motions are taking place along the line of motion of the moving hydrogen atom. For this situation, mark out the correct statement(s)

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. For $E\ge20.4\space eV$ only, collision would be elastic

  2. For $E\ge20.4\space eV$ only, collision would be inelastic

  3. For $E = 2.4\space eV$, collision would be perfectly inelastic

  4. For $E = 18\space eV$, the $KE$ of initially moving hydrogen atom after collision is zero

Show answer
Correct Option: B,D
Explanation:

K.E=2P.E
For electron in hydrogen to excite, a minimum of 10.2eV energy is required. Therefore, minimum 20.4eV K.E is required for inelastic collision otherwise, electron would not accept energy. And if E=20.4eV, collision would be perfectly inelastic.
If E is less than 20.4eV, collision is elastic and the two hydrogen atoms exchange velocities.
Therefore, B,D are the correct answers.

Regarding a nucleus, choose the correct options :

physics nuclei nuclear force the nuclear force nuclear force and binding energy

  1. Density of a nucleus is directly proportional to mass number A.

  2. Nucleus radius $ \propto {{A}^{1/3}}$

  3. Nuclear forces are dependent on the nature of nucleons.

  4. Nuclear forces are short range forces.

Show answer
Correct Option: B,D
Explanation:

Density of nucleus is: $\rho=\dfrac{A}{\dfrac{4}{3}\pi R^3}$
The radius of a nucleus, $R=r _0A^{1/3},$ so density of nucleus is independent of A and $R\propto {^3\sqrt{A}}$
The nuclear force is a short-range force because the distance between the nucleon is less than $0.7$ fermi (then the force is repulsive) and if greater than $10.7$ fermi (the force is attractive).

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