Determine the Q -value for the fusion reaction ⁴ He + ⁴ He ⁸ Be , and indicate whether this process is energetically favourable. The atomic mass of ⁸ Be is given as 8.0053 u , while that of ⁴ He is 4.0026 u .

Step-by-step solution

The Q -value of a nuclear reaction is given by the mass difference between reactants and products multiplied by c^2 . Q = ( m)c^2 = (2m_ He - m_ Be )c^2 Given m_ He = 4.0026 u and m_ Be = 8.0053 u . m = 2(4.0026) - 8.0053 m = 8.0052 - 8.0053 = -0.0001 u Converting this mass difference into energy using 1 u 931 MeV : Q = -0.0001 931 MeV = -0.0931 MeV = -93.1 keV Since the Q -value is negative, energy is absorbed in the reaction, making it an endothermic process. Thus, it is not energetically favourable.