10. A photon of energy 300 keV undergoes Compton scattering with a stationary electron. The photon is scattered at an angle of 90° relative to its initial direction.
(a) Calculate the initial wavelength of the photon. [2]
(b) Calculate the change in wavelength of the photon due to scattering. [2]
(c) Determine the energy of the scattered photon. [3]
(d) Explain why the Compton effect provides evidence for the particle nature of light. [2]
Question
Calculate the initial wavelength of the photon. [2]
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Use the formula relating photon energy and wavelength, E = hc/λ. Remember to convert the energy from keV to Joules first.
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\(\lambda_i \approx 4.14 \times 10^{-12}\) m
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Calculate the change in wavelength of the photon due to scattering. [2]
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Use the Compton scattering formula: Δλ = (h / (m_e c)) * (1 – cosθ). The scattering angle θ is 90°.
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\(\Delta\lambda = 2.43 \times 10^{-12}\) m
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Determine the energy of the scattered photon. [3]
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First, find the final wavelength (λ_f) by adding the change in wavelength (Δλ) to the initial wavelength (λ_i). Then, use the energy-wavelength relationship (E_f = hc/λ_f) to find the final energy.
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E_f ≈ 3.03 × 10^{-14} J (or 189 keV)
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Explain why the Compton effect provides evidence for the particle nature of light. [2]
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Contrast the prediction of classical wave theory (scattered wavelength = incident wavelength) with the experimental observation (scattered wavelength > incident wavelength, dependent on angle). Explain how the photon model (particle collision) accounts for this observation.
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Classical wave theory predicts scattered light has the same wavelength as incident light. Compton scattering shows wavelength increases (energy decreases) depending on scattering angle. This is explained by treating light as particles (photons) colliding with electrons, conserving energy and momentum, supporting light’s particle nature.
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