Mass-Energy Equivalence

Mass-Energy Equivalence

Mass and energy are two faces of the same quantity. The rest energy $E_0 = mc^2$ is staggeringly large:

• 1 gram of matter: $E_0 = 10^{-3} \times (3 \times 10^8)^2 \approx 9 \times 10^{13}$ J — roughly equivalent to 21 kilotons of TNT.

Nuclear Binding Energy

The mass of a nucleus is less than the sum of its constituent protons and neutrons. This mass defect $\Delta m$ is released as energy:

$\Delta E = \Delta m \cdot c^2$

Fusion in the Sun

Four protons (total mass $4 \times 1.6726 \times 10^{-27}$ kg) fuse to form a helium-4 nucleus (mass $6.6447 \times 10^{-27}$ kg). The mass defect:

$\Delta m = 4m_p - m_{\text{He}} = 4.57 \times 10^{-29}\ \text{kg}$

releases $\Delta E \approx 4.1 \times 10^{-12}$ J per fusion event — the energy that powers the Sun.

Your Task

Implement:

• mass_to_energy(m) — returns $E = mc^2$ in joules
• energy_to_mass(E) — returns $m = E/c^2$ in kg
• binding_energy(mass_parts, mass_nucleus) — returns $(\Delta m) c^2$ in joules

Use $c = 299792458.0$ m/s defined inside each function.