NUC-19

Bragg-peak snapshot

S(x) ≈ S₀ / (1 − x/R)^{0.4} for x < R. A pedagogical Bragg curve.

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NuclearBragg

Governing equation

S(x)\approx S_0(1-x/R)^{-0.4}

$x \in \left[0, 40\right]$

where

S_0: Entrance stopping (MeV/cm)
x: Depth (cm)
R: Range (cm)
S: Stopping at x (MeV/cm)

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

S(x)\approx S_0(1-x/R)^{-0.4}

$x \in \left[0, 40\right]$

$x = 0$ $S = 8$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0,\quad x_{\max} = 40

$x \in \left[0, 40\right]$

$x = 0$ $x = 0$

Along the curve

③

Response curve — green

S(x)\approx S_0(1-x/R)^{-0.4}

$x \in \left[0, 40\right]$

$x = 0$ $S = 8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}x}

$x \in \left[0, 40\right]$

$x = 0.252$ $S^{\prime} = 0.419$

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-19 — Bragg-peak snapshot) is the form associated with Bragg. Working symbols: $S_0$ , $x$ , $R$ $\rightarrow$ $S$ . Stopping rises as the particle slows, then drops to zero past the range. Hadron therapy sits here.

Purpose

Purpose: compute

S

from

S_0

x

R

in Nuclear physics via

S(x)\approx S_0(1-x/R)^{-0.4}

S(x) ≈ S₀ / (1 − x/R)^{0.4} for x < R. A pedagogical Bragg curve. 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

S_0 = 8.000\,\mathrm{MeV/cm}

x = 6.000\,\mathrm{cm}

R = 8.000\,\mathrm{cm}

, the governing relation

S(x)\approx S_0(1-x/R)^{-0.4}

yields

S = 13.93\,\mathrm{MeV/cm}

. A depth axis, a late peak. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Entrance stopping S_08 MeV/cmDepth x6 cmRange R8 cm

Outputs

Stopping at x S13.93 MeV/cm

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Narration of this film

A depth axis, a late peak.

Stopping rises as the particle slows, then drops to zero past the range. Hadron therapy sits here.

Reading speed

Watch on YouTube