Section 10.2: Quantum Theory
Quantum theory describes the behavior of particles at atomic and subatomic scales. Classical physics cannot explain certain phenomena, such as blackbody radiation and the photoelectric effect.
- Planck’s Hypothesis: Energy is quantized; it is emitted or absorbed in discrete amounts called quanta: \[ E = h \nu \] where \(h\) = Planck’s constant, \( \nu \) = frequency of radiation.
- Photoelectric Effect: Electrons are emitted from a metal surface when light of sufficient frequency shines on it; energy depends on frequency, not intensity.
- de Broglie Hypothesis: Particles have wave-like properties with wavelength: \[ \lambda = \frac{h}{p} \] where \(p\) = momentum of the particle.
- Heisenberg Uncertainty Principle: It is impossible to simultaneously know the exact position and momentum of a particle: \[ \Delta x \, \Delta p \geq \frac{h}{4\pi} \]
Example: Photon Energy
Calculate the energy of a photon with wavelength 500 nm.
\( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{500 \times 10^{-9}} \approx 3.97 \times 10^{-19} \, \text{J} \)
Practice Problems
- Calculate the wavelength of an electron moving with momentum 1.0 × 10^-24 kg·m/s.
- Explain why the photoelectric effect cannot be explained by classical wave theory.
- A photon has energy 2.0 × 10^-19 J. Determine its frequency.
- State the significance of Planck’s constant in quantum theory.
- Describe one consequence of the Heisenberg Uncertainty Principle for electrons in atoms.