Overview: Nuclei

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).

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

Where:

R₀ = 1.2 × 10⁻¹⁵ m = 1.2 

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

\[E=mc^2\]

Where:

• E = energy

• m = mass

• c = 3 × 10⁸ m/s

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

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

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

\[E_b=\Delta Mc^2\]

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

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

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.

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 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.

 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.

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

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 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