Calculating 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

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

Calculating Energy Released in Nuclear Reactions (CIE A Level Physics)