Introduction

Einstein's discovery that mass and energy are interchangeable forms of the same fundamental quantity revolutionized our understanding of physics. This principle, expressed through the famous equation $E = mc^2$, explains phenomena ranging from nuclear reactions in stars to particle physics interactions.

The Mass-Energy Relationship

In Einstein's special relativity, mass and energy are equivalent and interchangeable. This relationship is expressed by the equation:

$E = mc^2$

Where:

For practical calculations, we often use alternative units:

Solar Energy Production

The Sun generates energy through nuclear fusion, primarily through two processes:

1. The Proton-Proton Chain

[Insert PP-Chain Diagram]

In this process, four hydrogen nuclei (protons) combine to form one helium nucleus. The mass difference between reactants and products converts to energy:

The nuclear equation for this process is:

\4 ^1H \rightarrow ^4He + 2e^+ + 2\nu_e + 2\gamma$$

2. The CNO Cycle

This cycle uses carbon, nitrogen, and oxygen as catalysts to facilitate hydrogen fusion. The net result is identical to the proton-proton chain: four hydrogen nuclei combine to form one helium nucleus.

Particle-Antiparticle Annihilation

Electron-Positron Annihilation

When an electron meets its antiparticle (positron), they annihilate to produce two gamma-ray photons:

$e^- + e^+ \rightarrow 2\gamma$

Each photon carries energy of 0.511 MeV, for a total energy of:

$E_{total} = 2 × 0.511 \\= 1.022 \text{ MeV}$

Proton-Antiproton Annihilation

The annihilation of protons and antiprotons is more complex due to their composite nature. The total energy released is:

$E_{total} = (2 × 1.673 × 10^{-27})(3 × 10^8)^2 \\= 3.01 × 10^{-10} \text{ J} \\= 1880 \text{ MeV}$

Chemical Reactions and Mass Conservation

In chemical reactions like combustion, the mass difference between reactants and products is much smaller than in nuclear reactions. For example, the combustion of octane:

$C_8H_{18} + \frac{25}{2}O_2 \rightarrow 8CO_2 + 9H_2O$

The mass difference, while present, is typically too small to measure directly with conventional equipment.