Physics

Physics

Problem

Two photons are incident on free electrons. Photon X has initial wavelength 0.050 nm0.050\,\text{nm}, and Photon Y has initial wavelength 0.0050 nm0.0050\,\text{nm}. Both are scattered through an angle of 60∘60^{\circ}. Which photon experiences the larger percentage increase in wavelength, and why? Answer with “Photon X” or “Photon Y” followed by one concise reason.
Intuitive explanation

This is about Compton scattering, where a photon's wavelength increases when it collides with an electron. The key insight is that the absolute wavelength shift Δλ\Delta\lambda depends only on the scattering angle (via the Compton formula), not on the initial wavelength—so a photon starting with a shorter wavelength experiences a much larger percentage change. Since Photon Y begins much shorter, the same fixed shift represents a bigger fractional increase.

Photon Y — it has a smaller initial wavelength, so the fixed Compton shift produces a larger percentage increase.

Intuitive explanation

This is about Compton scattering, where a photon's wavelength increases when it collides with an electron. The key insight is that the absolute wavelength shift Δλ\Delta\lambda depends only on the scattering angle (via the Compton formula), not on the initial wavelength—so a photon starting with a shorter wavelength experiences a much larger percentage change. Since Photon Y begins much shorter, the same fixed shift represents a bigger fractional increase.

Photon Y — it has a smaller initial wavelength, so the fixed Compton shift produces a larger percentage increase.

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