What is nuclear fusion?

Why can fusion of light nuclei release energy?

Write the Q-value formula for a fusion reaction.

The deuterium-tritium reaction releases \(17.6\,\mathrm{MeV}\). Convert this to joules.

Balance the reaction \(^{2}_{1}\mathrm H+^{3}_{1}\mathrm H\to ^{4}_{2}\mathrm{He}+?\).

Why must fusing nuclei overcome or tunnel through a Coulomb barrier?

Write an approximate Coulomb barrier energy for two nuclei with charges \(Z_1e\) and \(Z_2e\) separated by \(r\).

Compare the Coulomb barrier for deuterium-tritium fusion with proton-carbon fusion using charge product \(Z_1Z_2\).

Estimate the thermal energy scale \(k_BT\) at \(T=1.0\times10^8\,\mathrm K\) in keV.

Why can fusion occur in stars even when average thermal energy is below a simple Coulomb-barrier estimate?

Explain why fusion rates are very temperature sensitive.

A fusion reaction has initial rest mass \(5.0302\,\mathrm u\) and final rest mass \(5.0113\,\mathrm u\). Find \(Q\).

In \(D+T\to \alpha+n\), why does the neutron carry a large fraction of the released energy?

For \(D+T\to \alpha+n\) with \(Q=17.6\,\mathrm{MeV}\), estimate neutron kinetic energy using product masses \(m_n\approx1u\) and \(m_\alpha\approx4u\).

Why is confinement needed for controlled fusion?

Explain qualitatively why the Lawson criterion involves density, temperature, and confinement time.

Why does fusion beyond the iron region not release energy in ordinary stellar burning?

A proposed fusion reaction has \(Q<0\). What does that imply about the total binding energy of products compared with reactants?

Use the tunneling estimate \(P\sim e^{-2\int\kappa dr}\) to explain why increasing charge product \(Z_1Z_2\) suppresses fusion.

Prove that fusion energy release can be written as \(Q=B_f-B_i\) when the same nucleons are rearranged.