Nuclear Binding Energy & Mass Deficit (Edexcel International A Level Physics)

• 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
  • m_p = mass of a proton (kg)
  • m_n = mass of a neutron (kg)
  • m_total = 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:

• 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

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