Nuclear Binding Energy
- Experiments into nuclear structure have found that the total mass of a nucleus is less than the sum of the masses of its constituent nucleons
- This difference in mass is known as the mass defect or mass deficit
- Mass defect is defined as:
The difference between the measured mass of a nucleus and the sum total of the masses of its constituents
- The mass defect Δm of a nucleus can be calculated using:
- Where:
- Z = proton number
- A = nucleon number
- mp = mass of a proton (kg)
- mn = mass of a neutron (kg)
- mtotal = measured mass of the nucleus (kg)
A system of separated nucleons has a greater mass than a system of bound nucleons
- Due to mass-energy equivalence, this decrease in mass implies that energy is released
- Energy and mass are proportional, so, the total energy of a nucleus is less than the sum of the energies of its constituent nucleons
- Binding energy is defined as:
The energy required to break a nucleus into its constituent protons and neutrons
- The formation of a nucleus from a system of isolated protons and neutrons therefore releases energy, making it an exothermic reaction
- This can be calculated using the equation:
Mass-Energy Equivalence
- Einstein showed in his Theory of Relativity that matter can be considered a form of energy and hence, he proposed:
- Mass can be converted into energy
- Energy can be converted into mass
- This is known as mass-energy equivalence, and can be summarised by the equation:
- Where:
- E = energy (J)
- m = mass (kg)
- c = the speed of light (m s-1)
- Some examples of mass-energy equivalence are:
- The fusion of hydrogen into helium in the centre of the sun
- The fission of uranium in nuclear power plants
- Nuclear weapons
- High-energy particle collisions in particle accelerators
Worked Example
The binding energy per nucleon is 7.98 MeV for an atom of Oxygen-16 (16O).
Determine an approximate value for the energy required, in MeV, to completely separate the nucleons of this atom.
Step 1: List the known quantities
-
- Binding energy per nucleon, E = 7.98 MeV
Step 2: State the number of nucleons
-
- The number of nucleons is 8 protons and 8 neutrons, therefore 16 nucleons in total
Step 3: Find the total binding energy
-
- The binding energy for oxygen-16 is:
7.98 × 16 = 127.7 MeV
Step 4: State the final answer
-
- The approximate total energy needed to completely separate this nucleus is 127.7 MeV
Exam Tip
Binding energy is named in a confusing way, so be careful!
Avoid describing the binding energy as the energy stored in the nucleus – this is not correct – it is energy that must be put into the nucleus to pull it apart.