Chapter 4: Mass-Energy Equivalence
E = mc². The most famous equation in physics states that mass and energy are equivalent and interconvertible. A small amount of mass contains an enormous amount of energy.
E = mc²
\( E = mc^2 \)
Rest energy of mass m
The Numbers
1 kg of mass = (1)(3×10⁸)² = 9×10¹⁶ J = 25 billion kWh!
This is the energy of about 20 megatons of TNT.
Nuclear Applications
Nuclear Fission
Heavy nuclei (uranium, plutonium) split into lighter fragments. The mass difference becomes kinetic energy. About 0.1% of mass is converted. Powers nuclear reactors and atomic bombs.
Nuclear Fusion
Light nuclei (hydrogen) fuse into heavier ones (helium). About 0.7% of mass is converted. Powers the Sun and stars. Potentially clean energy via fusion reactors.
Matter-Antimatter Annihilation
When matter meets antimatter, 100% of mass converts to energy (photons). 1 kg matter + 1 kg antimatter → 1.8×10¹⁷ J (43 megatons TNT equivalent).
Binding Energy and Mass Defect
A bound system has less mass than its components! The "missing" mass is the binding energy:
\( \Delta m = \frac{E_b}{c^2} \)
- • Hydrogen atom: mass 13.6 eV/c² less than proton + electron
- • Helium-4: mass 28.3 MeV/c² less than 2 protons + 2 neutrons
- • This "mass defect" is measurable and confirms E = mc²