Determine the Q -value for the fusion reaction: ²₁ H + ³₁ H ⁴₂ He + n Atomic masses are given as m(²₁ H ) = 2.014102 u , m(³₁ H ) = 3.016049 u , m(³₂ He ) = 3.016029 u , and m(⁴₂ He ) = 4.002603 u .

Step-by-step solution

The given fusion reaction is: ²₁ H + ³₁ H ⁴₂ He + n The total mass of the reactants is: m_ R = m(²₁ H ) + m(³₁ H ) m_ R = 2.014102 u + 3.016049 u = 5.030151 u The total mass of the products is: m_ P = m(⁴₂ He ) + m_ n Using the standard mass of a neutron, m_ n 1.008665 u : m_ P = 4.002603 u + 1.008665 u = 5.011268 u The mass defect m is: m = m_ R - m_ P m = 5.030151 u - 5.011268 u = 0.018883 u The Q -value of the reaction is calculated by converting the mass defect into energy (using 1 u 931.5 MeV ): Q = m 931.5 Me