6.10.1 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

• 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

Part (a)

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

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

xn_p = 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 = E_Sr + E_Xe – E_U

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