Revision: Class 12 >> Nuclei NEET (UG) Nuclei

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

`1/12`th of the mass of an atom of ₆C¹² isotope.

1 AMU is the average of proton rest mass and the neutron rest mass. Thus can be expressed as

1 AMU = 1.67377 × 10^-27 kg

= 1.67377 × 10^-24 gram

and C-12 is considered a reference for all atomic mass calculations.

The attractive force which holds the nucleons together in the nucleus is called nuclear force.

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

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 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 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.

A nuclear reaction is a process in which atoms collide with other atoms and lose some of their original mass.

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.

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

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

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

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

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

\[\Delta m_a=Am_p+Bm_n+Am_e-M_{ar}\]

\[BE=\Delta m\cdot c^2\]

\[E=mc^2\]

\[\Delta m=[ZM_p+(A-Z)M_n]-M_\mathrm{nucleus}\]

E_b = ΔM ⋅ c²

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

BE per nucleon ​= \[\frac {E.E.}{A}\]

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

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

V ∝ A

\[E=mc^2\]

\[\rho=\frac{3m}{4\pi R_0^3}\] (constant for all nuclei)

R = R₀​A^1/3

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

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

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

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

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

• 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.

• Mass of ₆C¹² is exactly 12 amu; 1 amu = 1.660565 × 10⁻²⁷ kg.
• 1 amu of mass, when converted to energy, gives 931.5 MeV.
• Mass defect arises because some mass is converted into binding energy that holds the nucleus together.
• Atomic mass = Number of protons + Number of neutrons.
• There are three fundamental particles of an atom: protons, neutrons, and electrons.
• Protons and neutrons are big-sized particles present in the nucleus of an atom.
• The density of the nucleus is independent of the mass number of the atom.

Mass defect refers to the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons (nucleons).

• 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.

• A nuclear reaction involves atoms colliding with other atoms and losing some of their original mass.
• Lost mass is converted into energy as per \[E=mc^2\].
• The two types of nuclear reactions used to produce energy are fission and fusion.

• 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.