(455) Binding energy E=mc^2 [IB Physics SL/HL]

Binding Energy

• Binding energy is the energy released when a nucleus is formed from its constituent parts.

• This is counterintuitive as energy is released during formation, not consumed.

Mass Defect

• The mass of reactants often differs from the mass of products in nuclear reactions, known as the mass defect.

• Example process: Hydrogen fusion into Helium in stars (PP Cycle).

Einstein's Equation

• E = mc² describes the relationship between mass and energy.

  • E: energy released (binding energy)

  • m: mass defect (missing mass)

• Mass defect gets converted into energy during nuclear reactions, producing light and heat.

Star Energy Production

• Stars convert hydrogen into helium, releasing energy observed as light and heat.

• This energy release is critical to stellar functionality.

Units of Measurement

• Energy is measured in electron volts (eV) or mega electron volts (MeV).

• Mass defect can be in kilograms or atomic mass units (U).

• 1 atomic mass unit defined based on carbon.

Examples in Nuclear Decay

• Radium-226 undergoes alpha decay to produce Radon-222 and an alpha particle (He-4).

• Breakdown of numerical values during decay process is crucial to understanding decay equations.

• Masses of radium and products must be calculated accurately, retaining precision.

Calculating Energy Release

• Use mass defect to find released energy:

  • Convert mass defect (in U) to energy using 931.5 MeV/c².

  • Energy released can simplify calculations when working with atomic mass units.

Summary of Key Calculations

• Left Side of reaction (mass of radium) 226.254 U.

• Right Side Mass: Radon (222.0176 U) + alpha particle (4.026 U).

• Total Right Side: 226.0439 U.

• Mass defect calculated as difference: ~0.0052 U.

• Energy released: E = 0.0052 U * 931.5 MeV/c² leads to approximately 4.48 MeV.