Overview: Nuclear Structure

• Rutherford showed that the nucleus is very small (≈10⁻¹⁵ m) and contains almost all the mass and positive charge of the atom.
• The proton–electron hypothesis suggested that the nucleus is made of protons and electrons.
• This hypothesis failed because electrons cannot exist inside the nucleus due to energy and magnetic moment problems.
• After the discovery of the neutron (1932), it was accepted that the nucleus contains protons and neutrons.
• Atomic number (Z) = number of protons, mass number (A) = protons + neutrons, and neutrons = A − Z.

• The radius of a nucleus is of the order of 10⁻¹⁵ m and is given by
  R = R₀A^1/3
  where R₀ = 1.2 × 10⁻¹⁵ m and A is the mass number.
• The nuclear radius increases with mass number, so heavier nuclei have larger radii.
• Nuclei are generally spherical in shape, with only small deviations (about 10%).
• The density of a nucleus is independent of mass number and is nearly the same for all nuclei.
• The average nuclear density is about 2 × 10¹⁷ kg m⁻³, showing that the nucleus is extremely dense.

• Atomic mass refers to the mass of a neutral atom and includes the mass of the nucleus, orbital electrons, and their binding energies.
• The unified atomic mass unit (u) is \[\frac {1}{12}\] of the mass of one ¹²C₆ atom; the mass of a carbon-12 atom is exactly 12 u.
• The value of 1 u in kilogram is
  1 u = 1.6605 × 10⁻²⁷ kg.
• Masses of fundamental particles are expressed in u; for example: proton ≈ 1.0073 u, neutron ≈ 1.0087 u, electron ≈ 0.0005486 u.
• The energy equivalent of 1 u (using E = mc²) is
  1 u = 931.5 MeV,
  which is widely used in nuclear physics.

The atoms of an element whose nuclei have the same number of protons but different number of neutrons are called the 'isotopes' of that element.

OR

Atoms having the same atomic number but different mass numbers are called isotopes. 

The nuclei which have the same number of nucleons, but different number of protons and different number of neutrons are called ‘isobars’.

OR

Elements with the same mass number (A) but with different atomic n.umbers (Z) are called isobars.

The nuclei having equal number of neutrons are called ‘isotones’.

OR

Atoms having equal number of neutrons (N) and called isotones.

• A nuclear reaction is a process in which a nucleus interacts with a particle, forming a new nucleus and one or more new particles, and is written as
  X + a → Y + b or X(a, b) Y.
• Nuclear reactions may involve emission or absorption of energy, called reaction energy or disintegration energy.
• In every nuclear reaction, charge, total number of nucleons (mass number), and total mass plus energy are conserved.