Nuclear reactions: Q-value and cross-section
Nuclear physics · Physics
Study notes
Worked example: Compute the Q-value of d + t → α + n using atomic masses (u): d = 2.014102, t = 3.016049, α = 4.002603, n = 1.008665. Step 1: Initial mass = 2.014102 + 3.016049 = 5.030151 u. Step 2: Final mass = 4.002603 + 1.008665 = 5.011268 u. Step 3: Δm = 0.018883 u; Q = 0.018883 × 931.5 MeV/u = 17.59 MeV. Step 4: Exoergic — this 17.6 MeV per reaction is ITER's energy source; the neutron carries 14.1 MeV, the alpha 3.5 MeV. Step 5: Cross-section peaks (~5 barns) at deuteron energy ~100 keV — the Gamow peak balances tunnelling against thermal spread in reactors. Conclusion: Q > 0 says fusion pays; σ(E) says at what energy it pays best — both needed to design a reactor.