Compton Wavelength from Δλ(θ)
Known incident X-ray line. Measure the scattered wavelength at several angles and recover λ_C from a fit of Δλ versus (1 − cos θ).
Goal
Determine λ_C = h/(m_e c) from Δλ = λ_C (1 − cos θ). The slope of Δλ versus (1 − cos θ) is λ_C.
Equipment
- X-ray line (known λ)
- Scatterer
- Spectrometer
- Goniometer
Experiment
Theory
Compton scattering off a quasi-free electron shifts the photon wavelength by an amount that depends only on θ, not on the incident λ. The bench hides Δλ, λ′ and the analytic curve. Incident λ is known. A spectrometer reports λ′ after you record.
Procedure
- Incident λ is fixed and known. You only change the scattering angle θ.
- Record. The spectrometer logs λ′ with small noise. There is no live Δλ or λ_C.
- The notebook computes Δλ = λ′ − λ and 1 − cos θ. Repeat for at least 6 angles from about 20° to 160°.
- Fit Δλ versus (1 − cos θ); the slope is λ_C in pm. Compare with the reference.
Conclusion
The fitted Compton wavelength agrees with h/(m_e c). Main uncertainties: spectrometer noise and treating the electron as free and at rest.