CBSE Class 12 Physics Notes Chapter 13 Nuclei

The study of atomic nuclei and their constituents and interactions comes under the field of physics known as Nuclear physics. 

• Rutherford demonstrated that the radius of a nucleus is 104 times smaller than the radius of an atom.
• The nucleus contains the entire positive charge and more than 99.9% of the mass of the atom.
• The nuclei are the central core of every atom and are composed of neutrons and protons.

• Protons are positively charged particles, while neutrons have no charge.
• For an electrically neutral atom, the number of protons and electrons are equal.

The stability or instability of a particular nucleus depends on the attractive nuclear force between the protons and neutrons and the repulsive electrical interactions among the protons. Unstable nuclei decay, transforming themselves spontaneously into other structures by a variety of decay processes. CBSE Class 12 Physics Chapter 13 Notes on Nuclei are given in the article below for easy preparation and understanding of the concepts involved.

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Class 12 Physics Chapter 13 Notes - Nuclei

Composition of Nucleus

• Nucleus are composite of protons and neutrons.
• Protons and neutrons in a nucleus are known as nucleons.
• The number of protons in a nucleus is known as as atomic number (Z).
• The sum of the number of protons and neutrons is known as the mass number (A).
• From the latest discoveries, protons and neutrons are made of elementary particles called Quarks.

Composition of Nucleus

Properties of Protons

• Protons are positively charged particles.
• The magnitude of charge of a proton is 1.6 x 10^-19 C.
• The mass of one proton is 1.67 x 10^-27 kg or 1.007276 u.
• The number of protons in a nucleus gives the atomic number.
• It has a magnetic moment of 2.79 nuclear magnetons.

Properties of Neutron

• Neutron has no charge.
• The mass of a neutron is 1.67 x 10^-27 kg or 1.008665 amu.
• Being neutral, it can neither be attracted nor repelled by the nucleus of the atom, so it can penetrate deep into the atom of a target.
• Neutron has low ionization power.
• Inside the nucleus, it is stable.
• A neutron outside the nucleus (free neutron) is unstable.
• The mean life of a free neutron is about 16.6 minutes (approx 1000 seconds).
• The magnetic moment of a neutron is -1.91 nuclear magnetons.

Types of Nuclei

• Isotopes: The atoms of elements having the same atomic number but different mass numbers are called isotopes.
• Isobars: The nuclei which have the same mass number but different atomic numbers are called isobars.
• Isotones: The nuclei having an equal number of neutrons are called isotones.

Types of Nuclei

Size of the Nucleus

• Nuclear Radius: Experimental results indicate that the nuclear radius is proportional to A1/3, where A is the mass number of the nucleus i.e.

R ∝ A^1/3 ⇒ R = R₀A^1/3

Where R₀ = 1.2 x 10^-15 m = 1.2 fm

• Nuclear Volume: The volume of the nucleus is given by

V = 4/3 πR³ = 4/3 πR₀A^1/3 ⇒ V ∝ A

• Nuclear Density: The mass per unit volume of a nucleus is called nuclear density.
  • It is constant and independent of the mass number of the nucleus.
  • The density of the nucleus, ⍴ = 2.38 x 10¹⁷ kg/m³

Nuclear Force

• Nuclear force is a strong attractive force between the nucleons in the atomic nucleus that holds the nucleons together.
• It arises due to the exchange of particles known as π-mesons.
• π-meson is a fundamental particle having a mass 270 times the mass of an electron.

Nuclear Force

Properties of Nuclear Forces

• They are short-range forces.
• They do not exist at large distances greater than 10^-15 m.
• They are the strongest forces in nature.
• These are the attractive forces that cause the stability of the nucleus.
• These forces are charge-independent.
• They are non-central forces.
• They are exchange forces.

Mass-Energy Equation

• Einstein showed that it is necessary to treat mass as another form of energy.
• He gave the famous mass-energy equivalence formula i.e.

E = mc²

Where

• E is the equivalent energy
• m is the mass of the particle
• c is the speed of light

Mass Defect

• It is found that the mass of a nucleus is always less than the sum of the masses of its constituent nucleons in the free state.
• The difference in the masses is called mass defect.
• Formula:

Δm = Sum of the masses of nucleons - Mass of Nucleus

Δm = {Zm_p + (A - Z)m_n} - M

Where

• m_p is the mass of the proton
• m_n is the mass of the neutron
• Z is the atomic number
• A is the mass number
• M is the mass of the nucleus

Nuclear Binding Energy

• The total energy required to disintegrate the nucleus into its constituent particles is called nuclear binding energy.
• It can also be defined as the energy equivalent to the mass defect of the nucleus.
• Formula:

B.E = Δm x 931 MeV

Where Δm is the mass defect in amu.

Binding Energy Per Nucleon

• The average energy required to release a nucleon from the nucleus is called binding energy per nucleon.
• It determines the stability of a nucleus.
• Binding energy per nucleon is directly proportional to the stability of the nucleus.
• Formula:

Binding energy per nucleon = (Δm x 931)/A

Where

• Δm is the mass defect
• A is the mass number

Binding Energy Curve

• It is a graph between binding energy per nucleon and the total number of nucleons (i.e. mass number A).
• Some nuclei with mass number A < 20 have larger binding energy per nucleon than their neighboring nuclei.
• For example ₂He⁴, ₄Be⁸, ₆C¹², ₈O¹⁶, and ₁₀Ne²⁰.
• These nuclei are more stable than neighboring nuclei.
• The binding energy per nucleon is the maximum for nuclei of mass number A = 56 (₂₆F⁵⁶).
• Its value is 8.8 MeV per nucleon.
• For nuclei having A > 56, the binding energy per nucleon gradually decreases.
• For uranium (A = 238), the value of binding energy per nucleon drops to 7.5 MeV.

Binding energy per nucleon curve

Nuclear Fission

• The process of splitting a heavy nucleus into two lighter nuclei of comparable masses with liberation of energy is called Nuclear Fission.
• Fission reaction of U²³⁵ :

₉₂U²³⁵ + ₀n¹ → ₉₂U²³⁶ → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + ₃₀n¹ + Q

• The energy released in U²³⁵ fission is about 200 MeV.
• Fission of U²³⁵ occurs by slow neutrons only (of energy about 1 eV) or even by thermal neutrons (of energy about 0.025 eV).
• The mass of the compound nucleus must be greater than the sum of masses of fission products.
• The binding energy of the compound nucleus must be less than that of the fission products.

Nuclear fission

Nuclear Fusion

• A process in which two very light nuclei combine to form a nucleus with a larger mass number along with the simultaneous release of a large amount of energy is called nuclear fusion.
• For fusion high pressure and high temperature are required and so the reaction is called a thermonuclear reaction.

Nuclear fusion

There are Some important List Of Top Physics Questions On Nuclei Asked In CBSE CLASS XII