Section 10.4: Wave-Particle Duality
Wave-particle duality is a fundamental concept in quantum physics. Particles such as electrons exhibit both wave-like and particle-like properties. Similarly, light exhibits both wave and particle behavior.
- De Broglie Hypothesis: All matter has a wavelength associated with its momentum: \[ \lambda = \frac{h}{p} = \frac{h}{mv} \] where \( \lambda \) = wavelength, \( h \) = Planck’s constant, \( m \) = mass, \( v \) = velocity.
- Light can behave as particles (photons) or waves depending on the experiment.
- Wave properties include diffraction and interference; particle properties include momentum transfer and quantized energy exchange.
Example: Electron Wavelength
Calculate the de Broglie wavelength of an electron moving at \( 2.0 \times 10^6 \, \text{m/s} \). Electron mass: \( 9.11 \times 10^{-31} \, \text{kg} \).
Momentum: \( p = mv = 9.11 \times 10^{-31} \cdot 2.0 \times 10^6 = 1.822 \times 10^{-24} \, \text{kg·m/s} \)
Wavelength: \( \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34}}{1.822 \times 10^{-24}} \approx 3.64 \times 10^{-10} \, \text{m} \)
Practice Problems
- Find the de Broglie wavelength of a proton moving at \( 1.0 \times 10^7 \, \text{m/s} \).
- Explain one experiment demonstrating the wave nature of electrons.
- Light has a wavelength of 500 nm. Calculate the momentum of a photon.
- Compare the wavelengths of an electron and a baseball (0.145 kg) both moving at 10 m/s.
- Describe why wave-particle duality challenges classical physics.