A stationary deuteron ( ²₁ H ) and a stationary triton ( ³₁ H ) undergo nuclear fusion to produce an alpha particle ( ⁴₂ He ) and a neutron ( ¹₀ n ). The binding energies per nucleon for the deuteron, triton, and alpha particle are 1.1 MeV , 2.6 MeV , and 7.5 MeV respectively. Assuming the initial kinetic energies of the reactants are negligible, the kinetic energy of the emitted neutron is:

Step-by-step solution

The fusion reaction is: ²₁ H + ³₁ H ⁴₂ He + ¹₀ n First, calculate the Q -value of the reaction, which is the difference between the total binding energy of the products and reactants. Note that a free neutron has zero binding energy. Total BE of reactants = BE (²₁ H ) + BE (³₁ H ) Total BE of reactants = (2 1.1) + (3 2.6) = 2.2 + 7.8 = 10 MeV Total BE of products = BE (⁴₂ He ) + BE (¹₀ n ) Total BE of products = (4 7.5) + 0 = 30 MeV Q = 30 - 10 = 20 MeV This energy is shared as kinetic energy between the alpha part