Modern Physics
Compton backscatter (180°)
At θ = 180° the wavelength shift is maximal (2λ_C).
Compton backscatter (180°) — interactive Modern Physics simulation. At θ = 180° the wavelength shift is maximal (2λ_C). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Backscatter
At θ = 180° the wavelength shift is maximal (2λ_C).
Backscattering at θ = 180° gives the maximum Compton shift Δλ_max = 2λ_C, because cos 180° = −1. The incident photon donates the most momentum to the recoiling electron; the scattered photon emerges with the longest wavelength and lowest energy. Compare this limit with smaller angles on the stage.
- Δλ_max = 2λ_C
- θ = 180°
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
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Scattering angle θ (°)
What you measure:
- Wavelength shift Δλ (pm)
How the investigation runs
- Open the compton-180 preset and press Reset. The incident X-ray wavelength is 0.05 nm; the scattering angle is fixed at 180°.
- Enable the wavelength-shift readout.
- Set the scattering angle for each trial (approaching 180°) and record the wavelength shift.
Governing equation
Compton Shift at Backscatter — Δλ = λ_C(1 − cos θ)
The Compton formula Δλ = (h/m_ec)(1 − cos θ) is maximized at θ = 180°, where (1 − cos θ) = 2, giving the largest possible wavelength shift: Δλ_max = 2h/(m_ec) ≈ 4.85 pm.
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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.
- At θ = 0° (no scattering at all), what would Δλ equal? Does that make physical sense for a photon that doesn't interact?
- 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 180
- Select the Compton setup
- Press Play
- Maximum Compton 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.