A set of X–ray scattering experiments is performed with a narrow beam of…
PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter
Problem
A set of X–ray scattering experiments is performed with a narrow beam of monochromatic X–rays incident on a target containing essentially free electrons. For a variety of scattering angles θ (measured between the directions of the incident and scattered radiation), the experimenters record the wavelength of the scattered photons.
Their data show that the change in wavelength Δλ is essentially zero for θ=0∘, increases steadily with angle, and reaches a maximum at θ=180∘. Moreover, for a fixed θ, Δλ is found to be independent of the incident wavelength, provided the wavelength is short enough that the electrons can be treated as free.
Answer the following questions about how these observations bear on competing models of electromagnetic radiation.
(a) Describe how the observed dependence of Δλ on the scattering angle θ contradicts the expectations of a purely classical wave description of electromagnetic radiation.
(b) Using qualitative arguments based on conservation of energy and linear momentum applied to individual quanta of light, explain why the photon model naturally predicts a non-zero Δλ that depends only on θ and fundamental constants, not on the incident wavelength.
(c) Identify the central assumption in classical wave theory that leads to its failure to account for the experimental observations, and discuss how abandoning this assumption resolves the discrepancy.