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# Consider the deuterium-tritium fusion reaction with the tritium nucleus at rest:$$\frac{2}{1} \mathrm{H}+\frac{3}{1} \mathrm{H} \longrightarrow_{2}^{4} \mathrm{He}+\frac{1}{0} \mathrm{n}$$(a) From Equation $13.1,$ estimate the required distance of closest approach. (b) What is the Coulomb potential energy (in electron volts) at this distance? (c) If the deuteron has just enough energy to reach the distance of closest approach, what is the final velocity of the combined deuterium and tritium nuclei in terms of the initial deuteron velocity, $v_{0} ?$ (d) Use energy methods to estimate the minimum initial deuteron energy required to achieve fusion. (e) Why does the fusion reaction occur at much lower deuteron energies than that calculated in (d)?

## (a) $2.70\times10^{-15}m$ (b) 720 KeV (c) $v_F=\frac{v_0 m_D}{m_D+m_T}$ (d) 1.2 MeV (e) Quantum tunneling can occur

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