Q-Value of Nuclear Reactions

Q-Value of Nuclear Reactions

The Q-value of a nuclear reaction is the energy released (or absorbed). It comes from Einstein's $E = mc^2$: the difference in total rest mass between reactants and products converts to kinetic energy.

$Q = (\sum m_{\text{reactants}} - \sum m_{\text{products}}) \times 931.494 \text{ MeV/u}$

where atomic mass unit $1\text{ u} = 931.494$ MeV/$c^2$.

• $Q > 0$: exothermic — energy is released (fission, fusion)
• $Q < 0$: endothermic — energy must be supplied

Famous Example: D + T Fusion

$^2\text{H} + ^3\text{H} \rightarrow ^4\text{He} + n$

$Q = (2.014102 + 3.016049 - 4.002602 - 1.008665) \times 931.494 = 17.59 \text{ MeV}$

Threshold Energy

For endothermic reactions ($Q < 0$), the beam projectile must carry a minimum threshold energy:

$E_{\text{th}} = |Q| \left(1 + \frac{m_{\text{beam}}}{m_{\text{target}}}\right)$

Your Task

Implement:

• q_value_MeV(m_reactants_total_u, m_products_total_u) — Q in MeV
• is_exothermic(m_reactants_total_u, m_products_total_u) — True if Q > 0
• threshold_energy_MeV(Q_MeV, m_beam_u, m_target_u) — threshold energy, or 0.0 if exothermic