RTH-18

Electron practical range

Rp (cm water) ≈ E(MeV)/2. The bedside rule of thumb.

Reading speed

ElectronsRule of thumb Rp

Governing equation

R_p\approx E/2

$E \in \left[4, 25\right]$

where

E: Beam energy (MeV)
R_p: Practical range (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\approx E/2

$E \in \left[4, 25\right]$

$E = 4$ $R_p = 2$

Along the curve

②

Domain of the variable — blue

E_{\min} = 4,\quad E_{\max} = 25

$E \in \left[4, 25\right]$

$E = 4$ $E = 4$

Along the curve

③

Response curve — green

R_p\approx E/2

$E \in \left[4, 25\right]$

$E = 4$ $R_p = 2$

Along the curve

④

Rate of change — amber

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

$E \in \left[4, 25\right]$

$E = 4.132$ $R_p^{\prime} = 0.5$

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-18 — Electron practical range) is the form associated with Rule of thumb Rp. Working symbols: $E$ $\rightarrow$ $R_p$ . A 9 MeV beam stops near 4.5 cm. Choose energy so Rp sits just beyond the target.

Purpose

Purpose: compute

R_p

from

E

in Radiotherapy via

R_p\approx E/2

Rp (cm water) ≈ E(MeV)/2. The bedside rule of thumb. 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 = 9.000\,\mathrm{MeV}

, the governing relation

R_p\approx E/2

yields

R_p = 4.50\,\mathrm{cm}

. A pencil of electrons dying at Rp. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Beam energy E9 MeV

Outputs

Practical range R_p4.50 cm

Reading speed

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Narration of this film

A pencil of electrons dying at Rp.

A 9 MeV beam stops near 4.5 cm. Choose energy so Rp sits just beyond the target.

Reading speed

Watch on YouTube