Section 7.5: Mass-Energy Equivalence
Mass and energy are equivalent, as described by Einstein’s famous equation: \[ E = mc^2 \] where \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light in vacuum.
- Even a small amount of mass corresponds to a large amount of energy.
- Important in nuclear reactions and particle physics.
- Binding energy of nuclei arises from mass defect.
Example: Energy from Mass
Calculate the energy released if 0.01 kg of matter is completely converted to energy.
\( E = mc^2 = 0.01 \times (3.0 \times 10^8)^2 \approx 9.0 \times 10^{14} \, \text{J} \)
Practice Problems
- Calculate the mass equivalent of 1.0 × 10¹⁵ J of energy.
- A nuclear reaction releases 4.0 × 10¹³ J. Find the mass defect.
- Explain the concept of binding energy in terms of mass-energy equivalence.
- Determine the energy released by converting 5 g of matter completely into energy.
- Discuss why mass-energy equivalence is crucial in nuclear power and weapons.