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

\lambda'-\lambda=\lambda_C(1-\cos\theta)

$\theta \in \left[0, 180\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\lambda'-\lambda=\lambda_C(1-\cos\theta)

$\theta \in \left[0, 180\right]$

$\theta = 0$ $\Delta\lambda = 0$

Along the curve

②

Domain of the variable — blue

\theta_{\min} = 0,\quad \theta_{\max} = 180

$\theta \in \left[0, 180\right]$

$\theta = 0$ $\theta = 0$

Along the curve

③

Response curve — green

\lambda'-\lambda=\lambda_C(1-\cos\theta)

$\theta \in \left[0, 180\right]$

$\theta = 0$ $\Delta\lambda = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta\lambda}{\mathrm{d}\theta}

$\theta \in \left[0, 180\right]$

$\theta = 1.132$ $\Delta\lambda^{\prime} = 8.37\times 10^{-4}$

Along the curve

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: $\lambda$ , $\theta$ $\rightarrow$ $\Delta\lambda$ , $\lambda'$ . λ_C = 2.426 pm. Energy form: E′ = E / (1 + (E/m c²)(1−cosθ)).

Purpose

Purpose: compute

\Delta\lambda

\lambda'

from

\lambda

\theta

in Nuclear physics via

\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

\lambda = 1.240\,\mathrm{pm}

\theta = 90.000\,\mathrm{^{\circ}}

, the governing relation

\lambda'-\lambda=\lambda_C(1-\cos\theta)

yields

\Delta\lambda = 2.4263\,\mathrm{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.

Calculator

Inputs

Incident λ \lambda1.24 pmScatter angle \theta90 °

Outputs

Shift \Delta\lambda2.4263 pm
Scattered λ \lambda'3.6663 pm

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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)).

Reading speed

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