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

When uranium-235 nuclei undergo fission by absorbing slow-moving neutrons, two reactions are possible:

(a) For reaction 2, identify the particle c, and state the number, x, of such particles produced in the reaction.

(b) The binding energy per nucleon, E, for a number of nuclides is given by the table below. Use the table to show that the energy  produced in reaction 1 is about 210 MeV.

(c) The energy produced in reaction 2 is 163 MeV. Suggest, with supporting reason, which one of the two reactions is more likely to happen.

Answer:

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, the 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