Compton Scattering: Maximum Shift at Backscatter

1 · Predict

A photon that scatters straight backward (180°) transfers the most possible momentum to the electron it hits. Does this backscatter case give the largest possible Compton wavelength shift?

• The maximum shift happens at some other angle.
• The shift is the same at all angles including 180°.
• Yes — 180° backscatter maximizes (1 − cos θ), giving the largest possible wavelength shift for any angle.

2 · Set Up

1. Open the compton-180 preset and press Reset. The incident X-ray wavelength is 0.05 nm; the scattering angle is fixed at 180°.
2. Enable the wavelength-shift readout.
3. Set the scattering angle for each trial (approaching 180°) and record the wavelength shift.

3 · Collect Data

Plot Δλ (y-axis) against scattering angle θ (x-axis) for your three trials. Does it look like it's leveling off near 180°?

4 · Analyze

1. For one trial, compute Δλ = (h/(m_ec))(1 − cos θ). Compare to the table. Confirm θ = 180° gives Δλ = 2h/(m_ec), the maximum possible value.
2. Explain, using (1 − cos θ), why 180° gives the maximum shift: cos(180°) = −1, so (1 − cos θ) reaches its largest possible value of 2 at that angle.

5 · Extend

1. At 180°, the photon reverses direction completely, transferring the maximum possible momentum to the electron (conservation of momentum). Explain why maximum momentum transfer corresponds to maximum energy loss (and therefore maximum wavelength increase) for the photon.
2. At θ = 0° (no scattering at all), what would Δλ equal? Does that make physical sense for a photon that doesn't interact?

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