Section 10.5: Nuclear Physics
Nuclear physics deals with the structure, properties, and reactions of atomic nuclei. Key concepts include binding energy, radioactive decay, fission, and fusion.
- Binding Energy: The energy required to separate a nucleus into its constituent protons and neutrons. \[ E_b = (\Delta m)c^2 \] where \( \Delta m \) = mass defect, \( c \) = speed of light.
- Radioactive Decay: The spontaneous transformation of a nucleus into a more stable one, emitting particles or energy. Types: alpha (\( \alpha \)), beta (\( \beta \)), gamma (\( \gamma \)) decay.
- Nuclear Fission: Splitting a heavy nucleus into smaller nuclei, releasing energy.
- Nuclear Fusion: Combining light nuclei to form a heavier nucleus, releasing energy.
Example: Binding Energy
Calculate the binding energy of a helium-4 nucleus with a mass defect of \( 0.030 \, \text{u} \). (\( 1 \, \text{u} = 1.6605 \times 10^{-27} \, \text{kg} \), \( c = 3.0 \times 10^8 \, \text{m/s} \))
\( \Delta m = 0.030 \times 1.6605 \times 10^{-27} \approx 4.9815 \times 10^{-29} \, \text{kg} \)
\( E_b = \Delta m c^2 = 4.9815 \times 10^{-29} \cdot (3.0 \times 10^8)^2 \approx 4.48 \times 10^{-12} \, \text{J} \)
Practice Problems
- A nucleus has a mass defect of 0.025 u. Calculate its binding energy.
- Identify the type of decay in the reaction: \( {}^{14}_6C \to {}^{14}_7N + \beta^- + \bar{\nu}_e \).
- Compare the energy released in fission of uranium-235 to fusion of deuterium nuclei.
- A radioactive isotope has a half-life of 5 hours. If you start with 80 g, how much remains after 15 hours?
- Explain why fusion is more prominent in stars than on Earth.