Nuclear Force: Definition, Types, Characteristics

The nuclear force is one of nature’s four fundamental forces, along with gravitational and electromagnetic forces. They are also known as strong forces since they are \(10\) million times stronger than chemical binding forces. Ernest Rutherford discovered the nucleus in an atom. He proposed that the nucleus is made up of nucleons (protons and neutrons), and \(99.9\%\) of the atom’s mass is concentrated in the nucleus.

Now, a question arises! Though protons have a positive charge and repulsive electrostatic Coulomb force exists between protons, how do two protons stay in the nucleus? The answer is “Nuclear force”. There exists a stronger attractive binding force in the nucleus, which is nuclear force. Imagine two brothers’ proton \(1\) and proton \(2\) fighting over some family issue. They stay in the same house (nucleus) but want to separate from the family due to mindset mismatch (Coulomb repulsive force). They still decided to stay in the same place because of the mother’s strong bond with the children and her love (attractive nuclear force). This real-life example explains the role of nuclear force in binding nucleons in the nucleus.

What are the range, types, and characteristics of Nuclear force? We will get the answers to all these questions in this article.

Study Fundamental Forces of Nature

Nuclear Force

The four fundamental forces that make up the universe are electromagnetic force, gravity, strong nuclear force, and weak nuclear force. The basic concept of force is well-known. We must apply force to an object when pushing or lifting it. Isaac Newton, the famed physicist who first defined force in his three laws of motion, also established the universal law of gravity.

We know that atom is the building block of matter. Every atom has a nucleus, and electrons orbit around it. Neutral Neutrons and positively charged protons make up the nucleus, and the nuclear force binds them together.

But wouldn’t the electromagnetic repulsion between protons cause it to burst open? The nuclear explosion does not occur because of a more powerful, alluring force – The Strong Nuclear Force!

Types of Nuclear Force

Nuclear Force is of two kinds. They are

1. Strong nuclear force
2. Weak nuclear force

1. Strong Nuclear Force

The strongest of all fundamental forces in nature is the strong nuclear force. As the name suggests, a Strong nuclear force does not depend on charge. However strong the force is, it does not affect electrons. It binds protons and neutrons inside a nucleus of an atom. It has a short range of \(10^{-15}\;\rm{m}\), comparable to the dimension of an atomic nucleus. It acts between proton-proton, neutron-neutron, and proton-neutron as it is a very short-range force.

2. Weak Nuclear Force

We have heard about one of the nuclear processes, called carbon dating, used in the archaeological survey. The radioactive carbon dating process is based on the decay of radioactive carbon atoms via the Weak nuclear force, or Beta decay. A neutron on supply of energy breaks in proton, electron, and an elementary particle called anti-neutrino.
The weak nuclear force is stronger than the gravitational force. The range of the weak nuclear force action is about \(10^{-16}\;\rm{m}\). That makes the weak nuclear force feeble than the strong nuclear force

Different Types of Nuclei

The nuclei have been classified based on the number of protons (atomic number) and the total number of nucleons (mass number) as follows:

(i) Isotopes: These are nuclei having the same atomic number \(Z\) but a different mass number \(A\).
E.g.
\(_1{H^1},{\,_1}{H^2},{\,_1}{H^3}\)
\(_8{O^{16}},{\,_8}{O^{17}},{\,_8}{O^{18}}\)
\(_2H{e^3},{\,_2}H{e^4}\)
\(_{17}C{l^{35}},{\,_{17}}C{l^{37}}\)
\(_{92}{U^{235}},{\,_{92}}{U^{238}}\)

(ii) Isobars: These are nuclei having the same mass number \(A\) but a different atomic number \(Z\).
E.g.
\(_1{H^3}\) and \(_2{He^3}\), \(_6{C^{14}}\) and \(_{\text{7}}{N^{14}}\), \(_8{O^{17}}\) and \(_9{F^{17}}\)

(iii) Isotones: These are nuclei with the same number of neutrons \(A – Z\) but a different atomic number \(Z\).
E.g.
\(_4B{e^9}\) and \(_5{B^{10}},{\,_6}{C^{13}}\) and \(_7{N^{14}},{\,_8}{O^{18}}\) and \(_9{F^{19}},{\,_3}L{i^7}\) and \(_{{4}}B{e^8},{\,_1}{H^3}\) and \(_{{2}}H{e^4}\)

(iv) Mirror nuclei: These nuclei have the same mass number \(A\) but with the proton number \(Z\) and neutron number \(A – Z\) interchanged.
E.g.
\(_1{H^3}\) and \(_{{2}}H{e^3}\), \(_3L{i^7}\) and \(_{{4}}B{e^7}\)

Characteristics of Nuclei

Forces that act between protons and neutrons and keep these nucleons bound in the nucleus are called nuclear forces.

Nuclear radius: The nuclear radius is proportional to \({A^{\frac{1}{3}}}\) where \(A\) is the mass number of the nucleus^, as revealed by experiments, i.e. \(R \propto {A^{\frac{1}{3}}}\) \( \Rightarrow R = {R_0}{A^{\frac{1}{3}}}\), where \({R_0} = 1.2 \times {10^{ – 15}}\,{\text{m}} = 1.2\,{\text{fm}}\).

Note:

1. Heavier nuclei are bigger than lighter nuclei.

Nuclear volume: The volume of the nucleus is given by \(V = \frac{4}{3}\pi \,{R^3} = \frac{4}{3}\pi \,R_0^3A\, \Rightarrow V \propto A\)

Nuclear density: Nuclear density is defined as the mass per unit volume of a nucleus.
Nuclear density \((\rho) = \frac{{{\text{Mass of nucleus}}}}{{{\text{Volume of nucleus}}}} = \frac{{mA}}{{\frac{4}{3}\pi {{({R_0}{A^{\frac{1}{3}}})}^3}}}\)
Where \(m =\) Average mass of a nucleon (\(=\) mass of proton \(+\) mass of neutron \( = 1.66 \times {10^{-27}}\,{\text{kg}}\)).
and \(A =\) Mass of nucleus
\( \Rightarrow \rho = \frac{{3\,{\text{m}}}}{{4\pi R_0^3}} = 2.38 \times {10^{17}}\,{\text{kg/}}{{\text{m}}^3}\)
Note:
1. \(\rho\)(Nuclear density) is independent of \(A\), which means \(\rho\) is the same of all atoms.
2. The density of a nucleus is maximum at its centre and decreases as we move outwards from the nucleus.

Characteristics of Nuclear force

• 1) The nuclear force acts only up to a certain distance. It is a short-range force and hence exhibits the property of saturation.  The force acts between two nucleons for a separation between them of the order of \(1\,{\text{fm}}({10^{ – 15}}\,{\text{m}})\) or less. Accordingly, a nucleon can interact with only a limited number of nucleons in its neighbourhood.
• 2) The nuclear force is strongly attractive. For a very small
• 3) When the separation between two nucleons is about \(0.5\,{\text{fm}}\), the nuclear force turns repulsive and hence the nucleus is prevented from total collapse, which causes the stability of the nucleus.

• 4) The nuclear force is charge independent. The force between two nucleons has the nearly same magnitude.
• 5) The nuclear force is non-central. i.e., the nuclear force between two nucleons does not act along the line joining their centres.
• 6)The nuclear force is spin-dependent. It is found that nuclear force between two nucleons having parallel spin is stronger than that between two nucleons having an antiparallel spin.
• 7) Nuclear forces are non-electric. Nuclear forces cannot have electrical nature. If it were so, the protons would repel one another, leading to nuclear disruption.

8) Nuclear forces are exchange forces.

According to Japanese scientist Hideki Yukawa, the nuclear force between the two nucleons results from the exchange of pi-mesons between the nucleons.

\(\pi -\) Mesons are of three types –

• 1. Positive \(\pi\) meson \((\pi^+)\)
• 2. negative \(\pi\) meson \((\pi^-)\)
• 3. neutral \(\pi\) meson \((\pi^0)\).

The force between nucleons like neutron and proton is due to the exchange of charged meson between them i.e.
\(p \to {\pi ^ + } + n,\,n \to p + {\pi ^ – }\)

The forces between pair of neutrons and a couple of protons are the result of the exchange of neutral meson \((\pi^0)\) between them, i.e. \(p \to p’ + {\pi ^0}\) and \(n \to n’ + {\pi ^0}\)

Thus the exchange of \(\pi\) meson between nucleons keeps the nucleons bound together. It is responsible for the nuclear forces.

Dog-Bone analogy (Meson theory)

The interactions of pions in the nucleus can be explained with the dog bone analogy. Consider two dogs are having a common bone clenched in between their teeth very firmly.  Similarly, we consider the two interacting nucleons in the nucleus to be bound by a strong nuclear force.

Both the dogs want to take the bone, so they cannot be divided easily. They are bound to each other with a strong, attractive force (the bone) though the dogs themselves are strong enemies. The pi-mesons play the same role as the common bone in between two nucleons.

Nuclear Stability

There are about \(1500\) known nuclides, out of which less than \(260\) are stable. Others decay to form other nuclides by emitting \(\alpha\), \(\beta -\) particles and \(\gamma -\) E.M. waves; hence, they are unstable. (This process is called radioactivity). Many factors determine the stability of the nucleus. Few such factors are given below:

(i) Neutron-proton Ratio \(\left( {\frac{N}{Z}\,{\text{Ratio}}} \right)\)

The atomic number \(Z\) is a measure of the chemical properties of an atom. The atomic mass number \(A\) determines the stability of an atom. The greatest stability for lighter nuclei is achieved when the number of protons and neutrons are approximately equal \((N \approx Z)\) i.e. \(\frac{N}{Z} = 1\)

For Heavy nuclei, more neutrons than protons decide stability. Heavy nuclei are neutron-rich compared to lighter nuclei (for heavy nuclei, the greater the number of positively charged protons in the nucleus, the greater is the repulsive electrical force between them. More neutrons are added to keep the nucleus stable because more neutrons provide the strong, attractive forces necessary.)

The figure shows a plot of \(N\) verses \(Z\) for the stable nuclei for mass numbers up to about \(A = 40\). The larger the value of \(Z\) the nuclear force, cannot hold the nuclei together against the electrical coulomb repulsion of the protons unless the number of neutrons exceeds the number of protons. At \(Bi(Z = 83,\,A = 209)\), the neutron number exceeds the atomic number as \(N – Z = 43\). No stable nuclides are having \(Z > 83\).

• Note:
• 1. The nuclide \(_{83}B{i^{209}}\) is the heaviest stable nucleus.
• 2. A nuclide above the stability line, i.e. having excess neutrons, decay through \(\beta^-\) emission (neutron changes into a proton). Thus increasing atomic number \(Z\) and decreasing neutron number \(N\) in \(\beta^-\) emission \(\frac{N}{Z}\) ratio decreases.

A nuclide below the line of stability has an excess number of protons. Therefore, we can say that the nuclide decays by \(\beta^+\) emission, which decreases \(Z\) and increases \(N\). The \(\frac{N}{Z}\) ratio increases in \(\beta^+\) emission.

(ii) Even/odd Numbers of \(Z\) or \(N\): The stability of nuclides depends on the number of protons and neutrons. It is found that \(60\%\) of stable nuclides have even \(Z\) and even \(N\).
An even-odd nucleus (even \(Z\) and odd \(N\)) or odd-even nuclide (odd \(Z\) and even \(N\)) is found to be lesser stable, while the odd-odd nucleus is found to be less stable.
Only five stable odd-odd nuclides are known: \(_1{H^2},{\,_3}L{i^6},{\,_5}B{e^{10}},{\,_7}{N^{14}}\) and \(_{{\text{75}}}T{a^{180}}\).

(iii) Binding Energy Per Nucleon: The nucleus’s stability is determined by the value of its binding energy per nucleon. The ratio of the binding energy of a nucleus to its mass number \(A\) is the binding energy per nucleon. The higher the value of binding energy per nucleon, the more stable the nucleus is.

Solved Examples on Nuclear Force

Q.1. The ratio of radii of nuclei \(_{13}^{27}Al\) and \(_{52}^{125}Te\) is approximately
(a) \(6 : 10\)
(b) \(13 : 52\)
(c) \(40 : 177\)
(d) \(14 : 7\)
Ans: (a) By using \(r \propto {A^{\frac{1}{3}}}\) \( \Rightarrow \frac{{{r_1}}}{{{r_2}}} = {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^{\frac{1}{3}}} = {\left( {\frac{{27}}{{125}}} \right)^{\frac{1}{3}}} = \frac{8}{5} = \frac{6}{{10}}\).

Q.2. Size of nucleus is of the order of
(a) \({10^{ – 10}}\,{\text{m}}\)
(b) \({10^{ – 15}}\,{\text{m}}\)
(c) \({10^{ – 12}}\,{\text{m}}\)
(d) \({10^{ – 19}}\,{\text{m}}\)
Ans: (b) Size of an atom is of the order of \(10^{-10}\;\rm{m}\), and the size of the nucleus is of the order of \(10^{-15}\;\rm{m}\).

Q.3. Which of the following pairs is an isobar
(a) \(_1{H^1}\) and \(_1{H^2}\)
(b) \(_1{H^2}\) and \(_1{H^3}\)
(c) \(_6{C^{12}}\) and \(_6{C^{13}}\)
(d) \(_{15}{P^{30}}\) and \(_{14}{Si^{30}}\)
Ans: (d) Nuclei having the same atomic mass number but a different atomic number are called isobar.

Q.4. \(\pi\) mesons can be
(a) \({\pi^+}\) or \({\pi^-}\)
(b) \({\pi^+}\) or \({\pi^0}\)
(c) \({\pi^-}\) or \({\pi^0}\)
(d) \({\pi^+},\,{\pi^-}\) or \({\pi^0}\)
Ans: (d) \(p \to {\pi ^ + } + n,\;n \to p + {\pi ^ – }\) and \(n \to n’ + {\pi ^0}\).

Q.5. Nuclear forces are
(a) Short ranged attractive and charge-independent
(b) Short ranged attractive and charge-dependent
(c) Long ranged repulsive and charge-independent
(d) Long ranged repulsive and charge-dependent
Ans: (a) Nuclear force is charge independent, and it also acts between two neutrons.

Q.6. Two nucleons are at a separation \(1 \times {10^{ – 15}}\,{\text{m}}\). The net force between them is \(F_1\) if both are neutrons, it is \(F_2\) if both are protons and \(F_3\) if one is a proton and the other is a neutron. In such a case
(a) \({F_2} > {F_1} > {F_3}\)
(b) \({F_1} = {F_2} = {F_3}\)
(c) \({F_1} = {F_2} > {F_3}\)
(d) \({F_1} = {F_3} > {F_2}\)
Ans: (b) Nuclear forces are charge independent.

Q.7. The force acting between proton and proton inside the nucleus is
(a) Coulombic
(b) Nuclear
(c) Both
(d) None of these
Ans: (c) Both Coulomb and nuclear force act inside the nucleus.

Summary

1. The strong nuclear force is the strongest among all fundamental forces in nature.
2. Nuclear forces are short-range forces and exhibit the property of saturation.
3. Nuclear forces are attractive forces and cause the stability of the nucleus.
4. These forces are charge independent.
5. Nuclear forces are non-central forces.

FAQs on Nuclear Force

Q.1. What is the basic cause of nuclear force?
Ans: The strong nuclear force is created between nucleons by the exchange of particles called mesons.

Q.2. Which is the strongest nuclear force?
Ans: The strongest nuclear forces exist between nucleons (protons and neutrons) inside an atom’s nucleus.

Q.3. How does nuclear force work?
Ans: Nuclear forces (also known as nuclear interactions) are the forces that act between two or more nucleons. They bind protons and neutrons (nucleons) in atomic nuclei. The nuclear force is about \(10\) million times stronger than the chemical binding that holds atoms together in molecules.

Q.4. What are the two types of nuclear forces?
Ans: Nuclear Force is of two types. They are
1. Strong nuclear force
2. Weak nuclear force

Q.5. What are the properties of nuclear forces?
Ans: The properties of nuclear forces are-
1. The nuclear force is the strongest force in nature.
2. Forces that keep the nucleons bound in the nucleus are called nuclear forces.
3. Nuclear forces are short-range forces. These do not exist at large distances greater than \(10^{-15}\,\rm{m}\).
4. These forces are charge independent and non-central.

Q.6. What is Yukawa theory of nuclear forces?
Ans: According to Japanese scientist Hideki Yukawa the nuclear force between the two nucleons results from the exchange of particles called mesons between the nucleons.

Q.7. Why is nuclear force saturated?
Ans: Nuclear force is saturated because it is a short-range force and falls off rapidly beyond a critical value. Nucleons interact only with their first neighbour and not beyond that, i.e., their strength becomes saturated over a short distance.

Study Force and Laws of Motion Here

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