Compton Scattering: A Shallow-Angle Comparison

1 · Predict

At small scattering angles, a photon barely changes direction. Does its wavelength shift also become vanishingly small as the angle approaches zero?

• Yes — as θ → 0°, (1 − cos θ) → 0, so the wavelength shift vanishes for a photon that barely scatters.
• The shift stays roughly constant even at small angles.
• The shift actually grows larger at small angles.

2 · Set Up

1. Open the compton-45 preset and press Reset. The incident X-ray wavelength is 0.08 nm; the scattering angle is fixed at 45°.
2. Enable the wavelength-shift readout.
3. Set the scattering angle for each trial (small angles) and record the wavelength shift.

3 · Collect Data

Plot Δλ (y-axis) against scattering angle θ (x-axis) for your three trials.

4 · Analyze

1. For one trial, compute Δλ = (h/(m_ec))(1 − cos θ). Compare to the table. Confirm the shift shrinks as θ decreases.
2. Explain why a nearly-undeflected photon (small θ) transfers very little momentum to the electron, and therefore loses very little energy — hence the tiny wavelength shift.

5 · Extend

1. Unlike this experiment's incident wavelength (0.08 nm, different from compton-90's 0.05 nm), the wavelength SHIFT Δλ at any given angle would be identical between the two experiments. Explain why the Compton formula makes the shift independent of the incoming photon's wavelength.
2. At very small angles, Δλ becomes hard to measure experimentally against the (much larger) incident wavelength. Explain why Compton scattering experiments typically use short-wavelength X-rays rather than visible light, where an already-tiny picometer-scale shift would be even less noticeable.

The Physics Behind This Experiment

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