Edexcel A Level Physics

Revision Notes

11.1 Nuclear Binding Energy & Mass Deficit

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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:

capital delta m space equals space Z m subscript p space plus space left parenthesis A space – space Z right parenthesis m subscript n space – space m subscript t o t a l end subscript

  • 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)

Binding Energy, downloadable AS & A Level Physics revision notes

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:

capital delta E space equals space capital delta m c squared

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:

capital delta E space equals space capital delta m c squared

  • 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.

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