AQA A Level Physics

Revision Notes

8.4.2 Mass Difference & Binding Energy

Mass Difference & 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
  • Mass defect is defined as:

The difference between an atom’s mass and the sum of the masses of its protons and neutrons

  • The mass defect Δm of a nucleus can be calculated using:

Δm = Zmp + (A – Z)mn – mtotal

  • 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)
  • Due to the equivalence of mass and energy, this decrease in mass implies that energy is released in the process
  • Since nuclei are made up of neutrons and protons, there are forces of repulsion between the positive protons
    • Therefore, it takes energy, ie. the binding energy, to hold nucleons together as a nucleus
  • Binding energy is defined as:

The energy required to break a nucleus into its constituent protons and neutrons

  • Energy and mass are proportional, so, the total energy of a nucleus is less than the sum of the energies of its constituent nucleons
  • The formation of a nucleus from a system of isolated protons and neutrons is therefore an exothermic reaction – meaning that it releases energy
  • This can be calculated using the equation:

E = Δmc2

Exam Tip

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.

Atomic Mass Unit (u)

  • The unified atomic mass unit (u) is roughly equal to the mass of one proton or neutron:
    • 1 u = 1.66 × 10−27 kg
  • It is sometimes abbreviated to a.m.u
  • This value will be given on your data sheet in the exam
  • The a.m.u is commonly used in nuclear physics to express the mass of subatomic particles. It is equal to 1/12 of the mass of the carbon-12 atom

Table of common particles with mass in a.m.uTable of common particles with mass in a.m.u, downloadable AS & A Level Physics revision notes

  • The mass of an atom in a.m.u is roughly equal to the sum of its protons and neutrons (nucleon number)
    • For example, the mass of Uranium-235 is roughly 235u

Worked Example

Estimate the mass of the nucleus of element Copernicium-285 in Kg.

Give your answer to 2 decimal places.

WE - amu answer image, downloadable AS & A Level Physics revision notes

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