7.1 Mass-energy equivalence (E = mc²)

Einstein's famous equation E = mc² revolutionized our understanding of the universe. It shows that mass and energy are interchangeable, with even tiny amounts of mass potentially releasing huge amounts of energy.

This principle underpins nuclear reactions, explaining how stars generate power and how nuclear weapons work. It's a cornerstone of modern physics, connecting the concepts of mass and energy in ways that impact our daily lives.

Fundamentals of Mass-Energy Equivalence

Einstein's Revolutionary Equation

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• Mass-energy equivalence establishes a fundamental relationship between an object's mass and its energy content
• Einstein's equation $E = mc²$ quantifies this relationship
  • $E$ represents the total energy of an object
  • $m$ represents the object's mass
  • $c$ is the speed of light in a vacuum, approximately $3 \times 10^8$ m/s
• The speed of light ($c$) is a constant in all inertial reference frames according to special relativity
• Rest mass is the intrinsic mass of an object when measured in its own rest frame
• Rest energy is the energy equivalent of an object's rest mass, calculated using $E_0 = mc²$

Mass and Energy Interchangeability

• Mass and energy are different forms of the same entity, interchangeable according to Einstein's equation
• A small amount of mass can be converted into an enormous amount of energy due to the large value of $c²$ ($9 \times 10^{16}$ m²/s²)
• Conversely, a large amount of energy is required to create even a small amount of mass
• This interchangeability is not noticeable in everyday life because of the large magnitude of $c²$
• However, in high-energy processes such as nuclear reactions, the conversion between mass and energy becomes significant

Applications and Implications

Nuclear Reactions and Binding Energy

• Energy-mass conversion plays a crucial role in nuclear reactions, including fission and fusion
• In nuclear fission, a heavy nucleus splits into lighter nuclei, releasing energy due to the difference in binding energy
  • Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons
  • The binding energy per nucleon is greater for the products of fission than for the original heavy nucleus, resulting in a net release of energy
• In nuclear fusion, light nuclei combine to form a heavier nucleus, releasing energy if the binding energy per nucleon of the product is greater than that of the reactants (e.g., fusion of hydrogen into helium in the Sun)

Practical Applications and Theoretical Implications

• Mass-energy equivalence has practical applications in nuclear power generation and nuclear weapons
  • In nuclear power plants, the energy released from fission reactions is harnessed to generate electricity
  • Nuclear weapons rely on the rapid release of energy from fission or fusion reactions, resulting in destructive explosions
• The principle also has implications for the nature of matter and energy in the universe
  • It suggests that matter and energy are fundamentally interchangeable and that the total amount of matter plus energy in the universe is conserved
• Mass-energy equivalence is a key component of the theory of special relativity and has been experimentally verified through phenomena such as nuclear reactions and particle accelerator experiments