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NUC-07

Compton shift

λ′ − λ = (h/m_e c)(1 − cos θ). Wavelength shift of a scattered photon.

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NuclearCompton

Governing equation

λ′−λ=λC(1−cos⁡θ)\lambda'-\lambda=\lambda_C(1-\cos\theta)

where

\lambda
Incident λ (pm)
\theta
Scatter angle (°)
\Delta\lambda
Shift (pm)
\lambda'
Scattered λ (pm)

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-07 — Compton shift) is the form associated with Compton. Working symbols: λ\lambda, θ\theta →\rightarrow Δλ\Delta\lambda, λ′\lambda'. λ_C = 2.426 pm. Energy form: E′ = E / (1 + (E/m c²)(1−cosθ)).

Purpose

Purpose: compute Δλ\Delta\lambda, λ′\lambda' from λ\lambda, θ\theta in Nuclear physics via λ′−λ=λC(1−cos⁡θ)\lambda'-\lambda=\lambda_C(1-\cos\theta) λ′ − λ = (h/m_e c)(1 − cos θ). Wavelength shift of a scattered photon. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given λ=1.240 pm\lambda = 1.240\,\mathrm{pm}, θ=90.000 ∘\theta = 90.000\,\mathrm{^{\circ}}, the governing relation λ′−λ=λC(1−cos⁡θ)\lambda'-\lambda=\lambda_C(1-\cos\theta) yields Δλ=2.4263 pm\Delta\lambda = 2.4263\,\mathrm{pm}, λ′=3.6663 pm\lambda' = 3.6663\,\mathrm{pm}. A photon, an electron, a kinked ray. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Shift \Delta\lambda2.4263 pm
  • Scattered λ \lambda'3.6663 pm
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NUC-07 · spectrum
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Narration of this film

A photon, an electron, a kinked ray.

λ_C = 2.426 pm. Energy form: E′ = E / (1 + (E/m c²)(1−cosθ)).

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Watch on YouTube