(455) HL Wave particle duality [IB Physics HL]

Wave-Particle Duality

• Concept introduced by Louis de Broglie.

• Light behaves as both a particle and a wave; this is known as duality.

• Particle Behavior: Example - the photoelectric effect.

• Wave Behavior: Example - diffraction.

• Matter (e.g., electrons) also displays wave behavior.

Key Equation

• Wavelength Equation:

  • Lambda (λ) = H / P

  • Where:

    • λ = Wavelength (meters)

    • H = Planck's constant (6.63 × 10^-34 Js)

    • P = Momentum (kg·m/s)

Momentum of Light

• Light has momentum despite having no mass; uses H/λ for calculation.

• Impulse Equation: J = FΔt = ΔP

• Light can exert pressure, e.g., solar sails utilizing photon momentum.

Practical Examples

• Example 1:

  • Light Frequency: 457 kHz.

  • Calculate Wavelength:

    • v = fλ leads to λ = C/f (C = speed of light = 3 × 10^8 m/s).

  • Wavelength λ calculated to be 656,455 m (very large).

  • Momentum P found using λ: P = H / λ ≈ 1.01 × 10^-36 kg·m/s.

• Example 2:

  • Mass of Ball = 61 kg, Speed = 5.1 m/s.

  • Wavelength: λ = H / P, with P = MV.

  • Calculated λ ≈ 2.1 × 10^-34 m, indicating no concern for diffraction due to its size.