RTH-19

Electron Rp (empirical)

Rp = 0.521 E − 0.376 (cm water, E in MeV). ICRU-style fit.

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ElectronsICRU 35

Governing equation

R_p=0.521\,E-0.376

$E \in \left[2, 30\right]$

where

E: Mean incident energy (MeV)
R_p: Practical range Rp (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

R_p=0.521\,E-0.376

$E \in \left[2, 30\right]$

$E = 2$ $R_p = 0.666$

Along the curve

②

Domain of the variable — blue

E_{\min} = 2,\quad E_{\max} = 30

$E \in \left[2, 30\right]$

$E = 2$ $E = 2$

Along the curve

③

Response curve — green

R_p=0.521\,E-0.376

$E \in \left[2, 30\right]$

$E = 2$ $R_p = 0.666$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_p}{\mathrm{d}E}

$E \in \left[2, 30\right]$

$E = 2.176$ $R_p^{\prime} = 0.521$

Along the curve

Lecture brief

Historical brief

The linear-quadratic model, BED, tissue-maximum ratio and Clarkson scatter turned radiotherapy into fraction arithmetic. MU calculation on these sheets is that clinical closed form. This sheet (RTH-19 — Electron Rp (empirical)) is the form associated with ICRU 35. Working symbols: $E$ $\rightarrow$ $R_p$ . Rp is the intercept of the tangent at the steepest fall-off with the bremsstrahlung tail.

Purpose

Purpose: compute

R_p

from

E

in Radiotherapy via

R_p=0.521\,E-0.376

Rp = 0.521 E − 0.376 (cm water, E in MeV). ICRU-style fit. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 12.000\,\mathrm{MeV}

, the governing relation

R_p=0.521\,E-0.376

yields

R_p = 5.876\,\mathrm{cm}

. A PDD fall-off and a tangent hitting the axis. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mean incident energy E12 MeV

Outputs

Practical range Rp R_p5.876 cm

Reading speed

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Narration of this film

A PDD fall-off and a tangent hitting the axis.

Rp is the intercept of the tangent at the steepest fall-off with the bremsstrahlung tail.

Reading speed

Watch on YouTube