Revision: Atoms and Nuclei >> Nuclei Physics Science (English Medium) Class 12 CBSE

Both the proton and neutron together constitute the nucleus. They are called nucleons.

In a graph plotting binding energy per nucleon (Bₙ) against mass number (A) for all known nuclei, the resulting curve is called binding energy curve.

The energy equivalent to that of mass defect, i.e., the energy required for holding the nucleons together in a nucleus, is called the Binding Energy of the nucleus.

The minimum energy required to make an electron free from the nucleus is called the Binding Energy of an electron.

The minimum amount of energy required to be given to an electron in the ground state of an atom to set the electron free is called the Ionization Energy of that atom.

The ratio of the binding energy \[E_n\]_​ of a nucleus to the number of nucleons A in that nucleus is called Binding Energy Per Nucleon.

The energy required to take an electron from the ground state to an excited state is called the Excitation Energy of the electron in that state.

The definite amount of energies associated with the electrons in different orbits of an atom are called the Energy Levels (of that atom).

Radioactivity is a nuclear phenomenon. It is the process of spontaneous emission of α or β and γ radiations from the nucleus of atoms during their decay.

As nucleus is positively charged it strongly attracts the negative charged electrons. The electron orbit close to the nucleus are tightly bound by strong attractive force of nucleus. These electrons are known as bound electrons.

The phenomenon of spontaneous disintegration of an unstable nucleus of a naturally occurring isotope accompanied by emission of active radiations, α particles, β particles and γ radiations is called radioactivity.

Electrons in outer orbits are weakly bound with the nucleus. In solids these weakly bound electrons leave their individual atom and become a part of it. These electrons are known as free electrons.

The difference between the sum of the masses of the nucleons composing a nucleus and the rest mass of the nucleus is called the mass defect.

The energy released due to loss in mass during the processes of nuclear fission and fusion is called nuclear (or atomic) energy.

OR

The energy released when nuclei undergo a nuclear reaction (change in structure, forming new nuclei) is called nuclear energy.

OR

The energy released during the transformation of nuclei is called Nuclear Energy.

Nuclear fission is the process in which a heavy nucleus splits into two lighter nuclei of nearly the same size, when bombarded with slow neutrons. In each fission reaction, a tremendous amount of energy (≈ 190 MeV) is released.

OR

The process of splitting of a heavy nucleus (₉₂U²³⁵ or ₉₂U²³⁹) into two lighter nuclei of comparable masses along with the release of a large amount of energy after being bombarded by slow neutrons is called Nuclear Fission.

• Nuclear fusion is the process in which two light nuclei combine to form a heavy nucleus. In this process also, huge amount of energy is released.
• The phenomenon in which two light nuclei fuse to form a larger nucleus and energy is released is called Nuclear Fusion.

Nuclear fusion is the process in which two or more light nuclei combine to form a heavier nucleus, accompanied by the release of a large amount of energy.

Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei of nearly equal mass, accompanied by the release of a large amount of energy and neutrons.

The average energy required to remove one nucleon from the nucleus.

\[E_{bn}=\frac{E_b}{A}\]

Controlled thermonuclear fusion is the process in which steady power is generated by heating nuclear fuel to very high temperatures so that fusion reactions occur in a controlled manner.

The difference between the sum of masses of individual nucleons and the actual mass of the nucleus.

\[\Delta M=[Zm_p+(A-Z)m_n]-M\]

Atomic mass unit (u), defined as `1/12`th of the mass of the carbon (12C) atom. According to this definition, 

\[1\mathrm{u}=\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\]

\[=\frac{1.992647\times10^{-26}\mathrm{kg}}{12}\]

\[=1.660539\times10^{-27}\mathrm{kg}\]

Atomic number (Z) is defined as the number of protons present in the nucleus of an atom.

$Z=number\; of\; protons$

Neutron number (N) is defined as the number of neutrons present in the nucleus of an atom.

N = number of neutrons

Mass number (A) is defined as the total number of nucleons (protons and neutrons) present in the nucleus of an atom.

A = Z + N

Isotopes are atoms of the same element having the same atomic number (Z) but different mass numbers (A) or different neutron numbers (N).

Isobars are atoms of different elements having the same mass number (A) but different atomic numbers (Z).

Isotones are atoms of different elements having the same neutron number (N) but different atomic numbers (Z).

The process by which an unstable nucleus transforms into another nucleus by emitting radiation is called radioactive decay.

 Radioactivity is the phenomenon in which nuclei of a given species transform by giving out α, β, or γ rays.

α-rays are helium nuclei; β-rays are electrons. γ-rays are electromagnetic radiation of wavelengths shorter than X-rays.

Nuclear force is the strong attractive force of a totally different kind which binds protons and neutrons in the nucleus and overcomes the Coulomb repulsion between protons.

The energy required to separate a nucleus completely into its individual nucleons.

\[E_b=\Delta Mc^2\]

The nuclear radius is the distance from the centre of the nucleus to its surface.

\[q=+1.6\times10^{-19}\text{C}\]

\[m_p=1.6726\times10^{-27}\text{kg}\]

\[R=R_0A^{1/3}\]

where \[\mathrm R_{0}=1.4\times10^{-15}\mathrm{m}\]

\[\frac{R_1}{R_2}=\left(\frac{A_1}{A_2}\right)^{1/3}\]

BE per nucleon ​= \[\frac {E.E.}{A}\]

E_b = ΔM ⋅ c²

E_b ​= [(Zm_p​ + (A − Z)m_n​) − M] × c²

Binding Energy = \[(\Delta m)\cdot c^2=(\text{Mass defect})\cdot c^2\]

\[\text{Binding Energy per Nucleon}=\frac{\text{Binding Energy}}{\text{Nucleon Number}}\]

\[R=R_0A^{1/3}\]

Where:

R₀ = 1.2 × 10⁻¹⁵ m = 1.2 

\[E=mc^2\]

Where:

• E = energy

• m = mass

• c = 3 × 10⁸ m/s

 The Q-value of a nuclear process is

Q = final kinetic energy – initial kinetic energy.

Due to conservation of mass-energy, this is also,

Q = (sum of initial masses – sum of final masses)c²

\[\text{Fission Reaction of Uranium-235:}\_{92}\mathrm{U}^{235}+_0n^1\longrightarrow\left[_{92}\mathrm{U}^{236}\right]\longrightarrow_{56}\mathrm{Ba}^{144}+_{36}\mathrm{Kr}^{89}+3_0n^1+200\mathrm{~MeV}\]

\[_1\mathrm{H}^2+_1\mathrm{H}^2\longrightarrow_2\mathrm{He}^3+_0n^1+3.27\mathrm{~MeV}\]

\[_1\mathrm{H}^2+_1\mathrm{H}^2\longrightarrow_1\mathrm{H}\mathrm{e}^3+_1\mathrm{H}^1+4.03\mathrm{~MeV}\]

\[_1\mathrm{H}^2+_1\mathrm{H}^3\longrightarrow_2\mathrm{H}\mathrm{e}^4+_0n^1+17.59\mathrm{~MeV}\]

\[_1\mathrm{H}^2+_2\mathrm{He}^3\longrightarrow_2\mathrm{He}^4+_1\mathrm{H}^1+18.3\mathrm{~MeV}\]

• All atomic nuclei are made up of elementary particles called protons and neutrons.
• Protons are positively charged particles with charge 1.6 × 10⁻¹⁹ C.
• The mass of a neutron is slightly greater than that of a proton.
• Neutrons are electrically neutral (uncharged) particles.
• The number of protons in the nucleus of an element equals the number of electrons in the neutral atom.
• All nuclei of a given element may not have the same number of neutrons.

• Nuclear size is measured using the Rutherford scattering experiment.
• Alpha particles deflected at distances ~10⁻¹⁴ m.
• Fast electrons and neutron scattering are also used for measurement.
• Nuclear radius is expressed using the radius parameter \[R_0\]
• Nucleus size is extremely small compared to an atom.
• Nuclear density remains constant for all nuclei.

• The greater the binding energy per nucleon, the more stable the nucleus.
• Iron-56 (Fe⁵⁶) and Nickel-62 are among the most stable nuclei, lying at the peak of the binding energy curve.
• Light nuclei (A < 20): Binding energy per nucleon increases rapidly with mass number.
• Intermediate nuclei (A ≈ 20–60): Highest binding energy per nucleon — most stable region.
• Heavy nuclei (A > 60): Binding energy per nucleon gradually decreases — less tightly bound.
• Very heavy nuclei can become unstable and may undergo fission, splitting into smaller, more stable nuclei, releasing energy.
• If nucleons are separated, the energy required to separate them gets converted into mass.

• In a fission reaction, a heavy atomic nucleus is split into smaller nuclei, other particles and radiation.
• Uranium-235 absorbs a neutron and splits into barium and krypton, emitting neutrons and radiation.
• Each fission of U²³⁵ releases approximately 200 MeV of energy.
• 3 neutrons are released per fission, which can trigger further fissions — leading to a chain reaction.
• Nuclear power plants exploit the process of fission to create energy.
• If an incoming neutron strikes a uranium nucleus, fragments produced are chemical elements like barium or krypton, while some are free neutrons.

• In a fusion reaction, two or more light atomic nuclei fuse to form a single heavier nucleus.
• The mass change in the process is the source of nuclear energy.
• Fusion within the cores of the sun and other stars generates their radiating energy by fusing two hydrogen atoms to produce a helium atom.
• The product nucleus has less mass than the total mass of the combining nuclei — the difference is released as energy.
• Fusion of deuterium (²H) and tritium (³H) produces helium-4 and releases 17.59 MeV — the most energy-rich reaction listed.
• Fusion releases far more energy per unit mass than fission.