Modern Physics
Compton scattering at 45°
Intermediate angle — scattered photon energy drops moderately.
Compton scattering at 45° — interactive Modern Physics simulation. Intermediate angle — scattered photon energy drops moderately. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Compton angle
Intermediate angle — scattered photon energy drops moderately.
At intermediate angles the wavelength shift Δλ = λ_C(1 − cos θ) lies between 0 and 2λ_C. Energy and momentum are shared between the scattered photon and the recoiling electron; neither particle is at rest after the collision. Use θ = 45° as a bridge between grazing and backscatter limits.
- Δλ = λ_C(1−cos θ)
- Energy shift
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
At small scattering angles, a photon barely changes direction. Does its wavelength shift also become vanishingly small as the angle approaches zero?
Predictions to weigh
- 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.
Variable roles
What you set:
- Scattering angle θ (°)
What you measure:
- Wavelength shift Δλ (pm)
How the investigation runs
- Open the compton-45 preset and press Reset. The incident X-ray wavelength is 0.08 nm; the scattering angle is fixed at 45°.
- Enable the wavelength-shift readout.
- Set the scattering angle for each trial (small angles) and record the wavelength shift.
Governing equation
Compton Shift at Small Angles — Δλ = λ_C(1 − cos θ)
As θ → 0°, (1 − cos θ) → 0, so Δλ → 0: a photon that barely changes direction barely loses energy, consistent with momentum conservation for a nearly-undisturbed collision.
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 the shift shrinks as θ decreases.
- 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.
Where this shows up beyond the lab
- 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.
- 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.
- 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 45
- Select the Compton setup
- Press Play
- Angle sets energy loss
- 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.