Energy & Mass Equation (OCR A Level Physics)

Revision Note

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Lindsay Gilmour



Energy & Mass 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:

E = mc2

  • 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

Energy Released in Nuclear Reactions

  • The binding energy is equal to the amount of energy released in forming the nucleus, and can be calculated using:

E = (Δm)c2

  • Where:
    • E = Binding energy released (J)
    • Δm = mass defect (kg)
    • c = speed of light (m s-1)

  • The daughter nuclei produced as a result of both fission and fusion have a higher binding energy per nucleon than the parent nuclei
  • Therefore, energy is released as a result of the mass difference between the parent nuclei and the daughter nuclei

Worked example

Part (a)

Step 1:            Balance the number of protons on each side (bottom number)

92 = (2 × 46) + xnp (where np is the number of protons in c)

xnp = 92 – 92 = 0

Therefore, c must be a neutron

Step 2:            Balance the number of nucleons on each side

235 + 1 = (2 × 116) + x

x = 235 + 1 – 232 = 4

Therefore, 4 neutrons are generated in the reaction

Part (b)

Step 1:            Find the binding energy of each nucleus

Total binding energy of each nucleus = Binding energy per nucleon × Mass number

Binding energy of 95Sr = 8.74 × 95 = 830.3 MeV

Binding energy of 139Xe = 8.39 × 139 = 1166.21 MeV

Binding energy of 235U = 7.60 × 235 = 1786 MeV

Step 2:            Calculate the difference in energy between the products and reactants

Energy released in reaction 1 = ESr + EXe – EU

Energy released in reaction 1 = 830.3 + 1166.21 – 1786

Energy released in reaction 1 = 210.5 MeV

Part (c)

    • Since reaction 1 releases more energy than reaction 2, its end products will have a higher binding energy per nucleon
      • Hence, they will be more stable

    • This is because the more energy is released, the further it moves up the graph of binding energy per nucleon against nucleon number (A)
      • Since at high values of A, binding energy per nucleon gradually decreases with A

    • Nuclear reactions will tend to favour the more stable route, therefore, reaction 1 is more likely to happen

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Lindsay Gilmour

Author: Lindsay Gilmour

Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.

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