Nuclear Binding Energy

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.

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

Where:

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

E_b ​= ΔMc²

Where:

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

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

Where:

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

The graph of binding energy per nucleon versus mass number A.

Main Observations from the Graph

• For very light nuclei, the binding energy per nucleon is small.
• It rises sharply at low mass numbers.
• For nuclei with approximately 30 < A < 170, the binding energy per nucleon is nearly constant and lies around 8.0 to 9.0 MeV.
• Very heavy nuclei have slightly lower binding energy per nucleon than medium-mass nuclei.

This Means

• Medium-mass nuclei are generally the most stable.
• Very light nuclei can release energy by fusion.
• Very heavy nuclei can release energy by fission.

Some Nuclei Are Stable

A nucleus is stable when its nucleons are strongly bound together. Stronger binding generally corresponds to higher binding energy per nucleon.

Saturation Property of Nuclear Force

The source material notes that the near-constant value of binding energy per nucleon for a wide range of nuclei suggests an important property of the nuclear force called saturation. This means each nucleon interacts strongly only with a limited number of nearby nucleons, not with all nucleons in the nucleus.