Formula used
The wavelength shift for Compton scattering is:
Δλ = (h / (m c)) (1 − cos θ)
Here, h is Planck’s constant, c is the speed of light, m is target rest mass, and θ is scattering angle.
The scattered wavelength is λ′ = λ + Δλ, where λ is the initial wavelength.
How to use this calculator
- Select the photon input type you prefer.
- Enter wavelength, energy, or frequency with units.
- Enter the scattering angle in degrees or radians.
- Select the target particle, or enter a custom mass.
- Press Calculate to see results above the form.
- Download CSV or PDF for reporting and sharing.
Example data table
| Initial wavelength (nm) | Angle (deg) | Target | Shift Δλ (pm) | Scattered wavelength λ′ (nm) |
|---|---|---|---|---|
| 0.071 | 45 | Electron | 0.7106 | 0.0717106 |
| 0.071 | 90 | Electron | 2.4263 | 0.0734263 |
| 0.071 | 180 | Electron | 4.8526 | 0.0758526 |
Examples assume free-particle scattering and ignore binding effects.
Compton Wavelength Shift Article
1) Compton scattering in photon experiments
Compton scattering describes how a photon transfers momentum to a free particle and leaves with a longer wavelength. It is routinely observed with X‑ray sources, γ‑ray sources, and well‑collimated detectors. In laboratory geometries, angles are set by rotating a detector arm while maintaining a fixed target and beam alignment.
2) What the wavelength shift represents
The computed shift Δλ is a geometry‑dependent signature of relativistic energy–momentum conservation. A larger Δλ means the scattered photon lost more energy to the target’s recoil. This calculator reports both Δλ and the scattered wavelength λ′ so you can compare predictions directly with measured spectra.
3) Typical values for an electron target
For electrons, the Compton wavelength λC equals about 2.426 pm. At θ = 90°, the shift equals λC because (1 − cosθ) = 1. At θ = 180°, the shift reaches the maximum 2λC ≈ 4.852 pm. These magnitudes are comparable to hard X‑ray wavelengths.
4) Angle dependence and practical ranges
The angle term (1 − cosθ) varies from 0 at 0° to 2 at 180°, so Δλ grows smoothly with scattering angle. For a fixed incident wavelength, the relative shift Δλ/λ is larger for shorter wavelengths. That is why Compton shifts are easiest to resolve for energetic photons and wide angles.
5) Switching between wavelength, energy, and frequency
In beamline work you may know energy (keV) from a monochromator, frequency from instrumentation, or wavelength from tabulated lines. The calculator converts your chosen input into λ using λ = hc/E or λ = c/f, then applies the Compton shift. This avoids manual unit conversions and rounding errors.
6) How target mass changes the outcome
The shift scales with 1/m, so heavier targets yield much smaller wavelength changes. A proton’s Compton wavelength is roughly 1.32 fm, making Δλ effectively negligible for most X‑ray setups. Use the target selector or a custom rest mass to model electron‑like, muon‑like, or heavier scattering regimes.
7) Interpreting the energy ratio
Along with wavelengths, the tool reports energies and the ratio E′/E. Since E = hc/λ, a larger λ′ implies a smaller E′. For fixed θ, shorter incident wavelengths produce a more noticeable fractional energy loss. This is useful when estimating detector thresholds, shielding needs, or expected spectral peak shifts.
8) Measurement tips for cleaner comparisons
For best agreement, use narrow energy bandwidth, minimize multiple scattering, and keep the target thin enough to reduce absorption while maintaining count rate. Record θ accurately and keep geometry consistent. If your material has strong binding effects, treat this result as an ideal free‑particle estimate and compare trends rather than expecting perfect absolute matching.
FAQs
1) What is the Compton wavelength shift?
It is the increase in photon wavelength after scattering, computed as Δλ = (h/(mc))(1 − cosθ). It depends on the target rest mass and the scattering angle.
2) Why does the shift become largest at 180°?
Because (1 − cosθ) reaches its maximum value of 2 at 180°. This corresponds to the strongest momentum reversal, producing the greatest photon energy loss and the largest Δλ.
3) Can I enter energy instead of wavelength?
Yes. The calculator converts energy to wavelength using λ = hc/E, then applies the Compton shift. This is convenient when your photon source is specified in eV, keV, or MeV.
4) What does choosing a proton or neutron change?
Heavier targets have much smaller Compton wavelengths, so the predicted Δλ becomes extremely small. For many X‑ray cases, shifts for protons or neutrons are effectively negligible.
5) Does this include electron binding effects in atoms?
No. It uses the ideal free‑particle Compton formula. In real materials, binding and Doppler broadening can modify line shapes. Use this as a baseline prediction for the main shift trend.
6) What does the ratio E′/E tell me?
It shows how much photon energy remains after scattering. A value closer to 1 means little energy loss; smaller values indicate stronger recoil energy transfer to the target.
7) Why is my measured shift different from the result?
Common causes include angle misalignment, finite energy resolution, multiple scattering, and target‑material effects. Check geometry, reduce background, and compare several angles to confirm the expected dependence.