Compton Scattering: Wavelength Shift at 90°

1 · Predict

An X-ray photon scatters off a free electron. Does the scattered photon's wavelength change, and if so, does the amount of shift depend on the scattering angle?

• Yes — the wavelength shift grows with the scattering angle, reaching its maximum at 180° (straight back).
• The wavelength shift is the same at every angle.
• The scattered photon's wavelength doesn't change (like classical wave scattering).

2 · Set Up

1. Open the compton-90 preset and press Reset. The incident X-ray wavelength is 0.05 nm.
2. Enable the wavelength-shift readout.
3. Set the scattering angle for each trial and record the wavelength shift.

3 · Collect Data

Plot Δλ (y-axis) against (1 − cos θ) (x-axis) for your three trials. Is the line straight through the origin?

4 · Analyze

1. For one trial, compute Δλ = (h/(m_ec))(1 − cos θ) using h = 6.626×10⁻³⁴ J·s, m_e = 9.109×10⁻³¹ kg, c = 3×10⁸ m/s. Compare to the table.
2. Notice Δλ doesn't depend on the incident wavelength at all — only on the angle. Explain why the Compton shift is the same whether the incoming X-ray is 0.05 nm or 0.5 nm.

5 · Extend

1. Compton's 1923 experiment was historic evidence that light behaves like particles (photons) with definite momentum, not just waves — a purely wave picture predicts no wavelength shift at all in scattering. Explain why a wavelength-DEPENDENT shift would have been impossible to explain classically.
2. The constant h/(m_ec) ≈ 2.43 pm is called the Compton wavelength of the electron. Explain why this sets the natural size scale for how much a photon's wavelength can shift when scattering off an electron.

The Physics Behind This Experiment

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