(455) HL Compton scattering [IB Physics HL]

Compton Scattering

  • Compton scattering demonstrates the wave-particle duality of photons.

  • Photons possess momentum without mass, represented by the equation: λ = H / P.

Key Experiment Overview

  • Named after Arthur Compton (1923) who investigated the scattering of photons by stationary electrons.

  • Light collides with an electron, causing it to move and altering the photon's wavelength.

  • Initial wavelength (BB_i) decreases while final wavelength (BB_f) increases, indicating a shift to a higher wavelength.

Significance of Observation

  • The increase in wavelength cannot be explained solely by wave theory, providing evidence for the particle nature of light.

Experiment Components

  • Incident photon with initial wavelength λ_i collides with a stationary electron.

  • After the collision, the photon is scattered at an angle θ resulting in a final wavelength λ_f.

Important Equation

  • Change in wavelength: Δλ = λ_f - λ_i = H / (m_e * c) * (1 - cos(θ))

    • H = Planck's constant (6.63 x 10^-34 J·s)

    • m_e = mass of the electron (9.11 x 10^-31 kg)

    • c = speed of light (3 x 10^8 m/s)

    • θ = scattering angle (in degrees)

Cosine Analysis

  • For θ = 0°: Δλ = 0 (no change in wavelength if angle is zero).

Example Calculation

  • Given: Incident wavelength (λ_i), scattered at θ = 90°

  • Rearranging the equation gives: λ_f = H / (m_e * c) * (1 - cos(θ)) + λ_i

  • With θ = 90°, cos(90°) = 0 ⇒ λ_f = H / (m_e * c) + λ_i.

Calculation Steps

  1. Substitute constants into H / (m_e * c).

  2. Ensure units are consistent (usually in meters or nanometers).

  3. Perform calculations to find λ_f.

Conclusion of Example

  • λ_f determined to be approximately 5.5259 x 10^-12 m or 0.055 nanometers.

  • Wavelength increased from 0.31 nanometers to 0.055 nanometers, consistent with expectation.