Modern Physics
Compton scattering at 90°
Change θ — watch Δλ = λ_C(1 − cos θ) grow with angle.
Scatter X-rays off electrons at 90 degrees in a Compton scattering simulation. Measure wavelength shift and connect to photon momentum transfer.
Compton scattering
Change θ — watch Δλ = λ_C(1 − cos θ) grow with angle.
An X-ray photon collides with a nearly free electron at rest. The scattered photon loses energy and its wavelength increases by Δλ = (h/mₑc)(1 − cos θ). At θ = 90° the shift equals the Compton wavelength λ_C ≈ 2.43 pm. Rotate θ and watch the dashed scattered ray and Δλ readout grow with angle — direct evidence that photons carry momentum.
- Δλ = λ_C(1−cos θ)
- Photon momentum
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- The wavelength shift is the same at every angle.
- Yes — the wavelength shift grows with the scattering angle, reaching its maximum at 180° (straight back).
- The scattered photon's wavelength doesn't change (like classical wave scattering).
Variable roles
What you set:
- Scattering angle θ (°)
What you measure:
- Wavelength shift Δλ (pm)
How the investigation runs
- Open the compton-90 preset and press Reset. The incident X-ray wavelength is 0.05 nm.
- Enable the wavelength-shift readout.
- Set the scattering angle for each trial and record the wavelength shift.
Governing equation
Compton Scattering Formula — Δλ = λ_C(1 − cos θ)
A photon scattering off a free electron shifts to a longer wavelength by Δλ = (h/m_ec)(1 − cos θ), depending only on the scattering angle θ — direct evidence that photons carry momentum like particles.
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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.
- 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.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — E.2 Quantum physics
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Compton 90
- Select the Compton setup
- Press Play
- Photon wavelength shift
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.