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

A different mass unit used for expressing atomic masses is the atomic mass unit (u), defined as one-twelfth of the mass of a carbon-12 atom, called atomic mass unit.

Mathematically: 1 u = \[\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\] = 1.660539 × 10⁻²⁷ kg

A new type of neutral particle whose mass is very nearly the same as that of a proton is called neutron.

A proton or a neutron is called a nucleon.

All nuclides with the same mass number are called isobars.

Nuclides with the same neutron number but different atomic number are called isotones.

Atomic species of the same element differing in mass are called isotopes.

The nucleus of the lightest atom of hydrogen, which has a relative abundance of 99.985%, is called the proton.

The nuclear radius is the effective distance from the centre of the nucleus to its outer boundary. Since the nucleus does not have a perfectly sharp surface, this radius is treated as an approximate effective value in physics.

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

`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.

Mass defect is the difference between:

• the sum of the masses of the constituent protons and neutrons, and
• the actual mass of the nucleus.

The binding energy of a nucleus is the minimum energy required to separate the nucleus completely into its constituent protons and neutrons.

Binding energy per nucleon is the average binding energy associated with each nucleon in the nucleus.

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

Nuclear fission is a neutron-induced nuclear reaction in which a heavy nucleus, such as uranium-235, breaks into two intermediate-mass nuclear fragments.

Nuclear fusion is the process in which light nuclei combine to form a more tightly bound heavier nucleus, and energy is released during the process.

Because both nuclei carry a positive charge, they repel each other through electrostatic force. This repulsion is called the Coulomb barrier in the context of fusion.

Thermonuclear fusion is fusion initiated by extremely high temperature, which gives nuclei enough kinetic energy to approach one another closely.

m_n​ = 1.00866 u = 1.6749 × 10⁻²⁷ kg

A = Z + N

Where:

• Z = atomic number = number of protons.
• N = neutron number = number of neutrons.
• A = mass number = total number of protons and neutrons.

m_p ​= 1.00727 u = 1.67262 × 10⁻²⁷ kg

The experimentally observed relation is: R = R₀A^1/3

where:

• R = radius of the nucleus
• R₀​ = radius constant
• A = mass number of the nucleus.

For nuclei,

• R₀ ≈ 1.2 × 10⁻¹⁵ m.

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

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

\[E=mc^2\]

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

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

Where:

• ΔM = mass defect
• m_p​ = mass of one proton
• m_n​ = mass of one neutron
• M = actual mass of the nucleus

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

Where:

• E_bn = binding energy per nucleon
• E_b​ = total binding energy of the nucleus
• A = mass number

E_b ​= ΔMc²

Where:

• E_b​ = binding energy
• ΔM = mass defect
• c = speed of light

\[E=mc^2\]

V ∝ A

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

R = R₀​A^1/3

• 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).

• 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.