Nuclear Physics: Nuclear Force, Radioactive Decay, Theory and Applications

Nuclear Physics is the branch of physics that deals with the study of atomic nuclei located at the center of an atom, their constituents, and the interactions that hold constituents of nuclei together in a nucleus.

• The constituents of a nucleus are protons and neutrons which are bounded together in the nucleus by a force called Nuclear force.
• Protons are positively charged particles and Neutrons are electrically neutral particles.
• The size of a nucleus is about 10000 times the size of an atom.
• Nuclear physics is different from atomic physics, which deals with the study of the atom as a whole, including its electrons.
• Applications of nuclear physics have been found in a variety of fields. Such as nuclear power, nuclear medicine, and nuclear weapons. These applications are studied in the field of nuclear engineering.
• Particle nuclear developed from nuclear physics which deals with the study of fundamental particles and forces that constitute matter and radiation.
• Nuclear astrophysics based on nuclear physics is essential to understanding how stars work and the origins of chemical elements.

Key Terms: Force, Nuclear Force, Radioactivity, atomic and nuclear physics, nuclear and particle physics, Law of radioactive decay, electrons, protons, neutrons, Nuclear fusion, Nuclear fission.

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What is Nuclear Physics?

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Nuclear Physics is the branch of physics that deals with the study of atomic nuclei and their constituents. It also deals with the study of interactions between the constituents that hold them together in a nucleus. Modern nuclear physics allows us to understand things like atomic stability, radioactive decay, nuclear fission, nuclear fusion, carbon dating, etc.

• Atoms are the fundamental unit of matter and define the structure of the elements. 
• They are made of three components namely - protons, electrons, and neutrons.
• The nucleus is an essential structural part that located at the center of an atom and it is made of Neutrons and Protons.
• From the latest discoveries, protons and neutrons are made of elementary particles called Quarks.
• Protons and neutrons in a nucleus are known as Nucleons.
• The sum of the number of protons and number of neutrons in a nucleus is called Mass number.
• In 1911, Ernest Rutherford discovered protons based on the Geiger-Marsden gold foil experiment. He also theorized that there must be a neutral particle in the nucleus. In 1932, James Chadwick confirmed the presence of neutrons.
• After that Dimitri Ivanenko and Werner Heisenberg proposed models for atomic nuclei which consist of protons and neutrons.

Structure of an atom

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Nuclear Size Detailed Video Explanation:

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Nuclear Physics Theory

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The constituent particles of nuclei are protons and neutrons. The properties of nuclei can either be explained by neutrons and protons interacting, or, more fundamentally, by quarks and gluons. Protons inside the nucleus is a positively charged particles and neutrons are electrically neutral particles. According to the rule of electricity, the positively charged protons must repel each other. This indicates that there must be a force holding the nucleus together. This force is called NulcearForce, one of the basic forces of nature.

.Composition of an atom and nucleus

What are Protons?

These are positively charged particles present within the atomic nuclei.

• Protons are 99.86% as big as neutrons.
• The magnitude of the charge on a proton is 1.6 x 10^-19 C.
• The mass of a proton is 1.67 x 10^-27 kg or 1.007276 u.
• The number of protons present in a nucleus is unique to the element. The number of protons of an element is known as Atomic Number. The elements are arranged in the Periodic Table according to the atomic number in ascending manner.
• The number of protons also determines the chemical nature of that particular element.
• Each proton is made up of three ‘quarks’- two ‘up’ quarks and one ‘down quark’. They are held together by a massless subatomic particle, named ‘Gluon’.

What are Neutrons?

Neutrons are uncharged subatomic particles.

• They are present in all atomic nuclei except Hydrogen nuclei.
• A Neutron’s mass is slightly greater than that of a proton.
• The mass of a proton is 1.67 x 10^-27 kg or 1.007276 u.
• It is made up of three quarks- one ‘up’ quark and two ‘down’ quarks.
• Being neutral, it is neither attracted nor repelled by the nucleus of the atom, so it can penetrate deep into the atom of a target.

Mass Number

The total number of protons and neutrons present in a nucleus is called the mass number. It is written as

A= Z+N

Where

• A= Mass Number,
• Z= No. of protons,
• N= No. of Neutrons

Isotopes, Isobars, Isotones, and Isomers

Radius of the Nucleus

The size of the nucleus varies linearly with the mass number(A). The radius of the nucleus is given by

\(R=R_oA^{1\over3}\)

Where

• R is the radius of the nucleus
• A is the mass number
• R_o is the empirical constant for all nuclei and is equal to 1.2 x 10^-15 m

Mass Defect

When we try to calculate the mass of an atomic nucleus it is always less than the total mass of protons and neutrons together. The mass which is missing is called the Mass Defect. The mass is lost during the formation of the nucleus.

The formula for Mass Defect is given below-

Δm = Zm_p + (A−Z) m_n − M

where

• M = mass of the nucleus
• Δm = the difference between the mass of the nucleons and the mass of the nucleus
• m_p = Mass of the Proton
• m_n = mass of the Neutron
• A = mass number
• Z = Atomic number

Nuclear Binding Energy

The total energy required to disintegrate the nucleus into its constituents particles is called Nuclear binding energy. This energy is equivalent to mass defect of the nucleus and it is given by

E_b = ΔmC²

If nuclear binding energy is in amu ( atomic mass unit), then it is given by

E_b = Δm x 931 MeV

Nuclear Binding Energy Per Nucleon

The average energy required to release a nucleon from a nucleus is called Binding energy per nucleon (E_bn). It is given by

E_bn​ = E_b/A

Packing Fraction

It is the ratio of the mass defect to the nucleons. It tells about the stability of the nucleus. The stability of the nucleus is proportional to the value of the packing fraction.

Packing Fraction= Mass Defect/ Nucleon

Or,

Packing fraction (f)= [Zm_p+(A−Z)m_n−A]/A

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Nuclear Forces

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Nuclear force is a strong attractive force between nucleons in the atomic nucleus that holds nucleons together. Nuclear force arises due to the exchange of particles known as π mesons between the nucleons. Some of the properties of Nuclear force are:

• Nuclear force is a strong fundamental force in nature.
• This force is mainly attractive.
• The nuclear force is charge independent. The nuclear force between proton-proton, proton-neutron, and neutron-neutron is the same.
• Nuclear force is short-range force i.e. of the order of 10^-15 m.
• The nuclear force is an exchange force.
• It is a non-central force.

Nuclear force

Nuclei Class 12 Important Notes PDF

Nuclei Class 12 Important Notes

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Radioactivity

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Radioactivity can be defined as the emission of particles and ionizing radiation due to the spontaneous breakdown of heavy atomic nuclei.

• The elements which show this phenomenon are called Radioactive elements.
• Units of radioactivity are Curie (Ci) and Rutherford (Rd)

Three types of rays emerge from radioactive elements:

1. Alpha rays (α- rays)
2. Beta rays (β- rays)
3. Gamma rays (γ- rays)

Alpha rays (α- rays)

An alpha particle is equivalent to a helium nucleus i.e. doubly ionized helium atom consisting of 2 protons and 2 neutrons. Some of the properties of alpha particles are:

• They have a positive charge equal to +2e.
• They have a rest mass equal to 4 times the mass of the proton.
• They are capable of producing a heating effect.
• They are deflected by an electric field, as well as a magnetic field.

Beta rays (β- rays)

A Beta particle is comparable to a fast-moving electron. Some of the properties of beta particles are:

• They have a negative charge equal to the charge of an electron.
• The rest mass of a Beta particle is equal to the mass of an electron.
• The penetration power of the beta particle is more than the alpha particle.
• They are deflected by electric and magnetic fields.

Gamma rays (γ- rays)

Gamma rays are the high energy packets of electromagnetic radiation i.e. high energy photons. Some of the properties of Gamma rays are:

• They have no charge.
• The relative rest mass of the gamma particle is zero.
• They travel at the speed of light.
• They are not deflected by electric and magnetic fields.

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Radioactive Decay Law

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Radioactive decay obeys the following laws:

• Radioactive decay is a spontaneous process.
• A nucleus will emit one alpha particle or one beta particle only at a time. Both are not emitted simultaneously and gamma rays follow the emission of alpha and beta particles.
• When a radioactive element decays by emitting an alpha particle, the position of the daughter element is down by two places in the periodic table.
• When a radioactive element decays by emitting a beta particle, the position of the daughter element is raised by one place in the periodic table.
• When a radioactive element decays by emitting a gamma particle, its position remains the same in the periodic table.

The rate of disintegration of a radioactive substance at any moment is directly proportional to the number of radioactive atoms present in that substance at that moment. If N₀ is the total number of nuclei, then the number of undecayed nuclei N after time t is given by

\(N=N_0e^{-\lambda t}\)

Where,  λ = decay constant.

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Application of Nuclear Physics

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Some important applications of nuclear physics are:

• Nuclear energy is an important part of energy production. Nuclear reactors are used for the production of nuclear energy.
• Nuclear fission reactions are performed in nuclear reactors to generate electricity.
• In medical diagnostics and cancer therapy, nuclear physics techniques have made significant contributions.
• The radioactive elements are used in radiation therapy where ionizing radiation can be used to detect and treat cancers and several blood disorders.
• The use of nuclear devices has changed the world's political boundaries and determined the outcome of wars.
• Reactors originally developed for naval use generate the majority of the world's nuclear energy.

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Things to Remember

• Nuclear Physics is a branch of Physics that deals with the study of the atomic nucleus, what it constitutes, and its interactions. 
• Atoms are the fundamental unit of matter. They are made up of protons, neutrons, electrons, and quarks. 
• Nuclear physics deals with the nucleus of an atom only while atomic physics deals with the entire atom which has a small dense nucleus and Electrons.
• An atom is made up of a positively charged nucleus and negatively charged electron clouds.
• The total number of protons and neutrons present in a nucleus is called the mass number.
• Nuclear Force is the short-range attractive force between protons and neutrons. The nuclear force is the strongest in the whole universe.
• Packing Fraction is the ratio of the mass defect to the nucleons. It tells about the stability of the nucleus.
• Radioactivity can be defined as the emission of particles and ionizing radiation due to the spontaneous breakdown of heavy atomic nuclei.
• Radioactivity is of three types: Alpha, Beta, and Gamma Radiation. 
• Half-time of a radioactive decay represents the time after which half of the original nuclei remain in the substance.
• Radioactive elements are used in radiation therapy where ionizing radiation can be used to detect and treat cancers and several blood disorders. Nuclear fission reactions are performed in the nuclear reactors to generate electricity.

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