NUC-18

α range in air

R ≈ 0.31 E^{3/2} cm for α in air at STP (E in MeV). Bragg–Kleeman sketch.

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NuclearBragg–Kleeman

Governing equation

R\approx 0.31\,E^{3/2}\,\mathrm{cm}

$E \in \left[1, 10\right]$

where

E: α energy (MeV)
R: Range in air (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\approx 0.31\,E^{3/2}\,\mathrm{cm}

$E \in \left[1, 10\right]$

$E = 1$ $R = 0.31$

Along the curve

②

Domain of the variable — blue

E_{\min} = 1,\quad E_{\max} = 10

$E \in \left[1, 10\right]$

$E = 1$ $E = 1$

Along the curve

③

Response curve — green

R\approx 0.31\,E^{3/2}\,\mathrm{cm}

$E \in \left[1, 10\right]$

$E = 1$ $R = 0.31$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R}{\mathrm{d}E}

$E \in \left[1, 10\right]$

$E = 1.057$ $R^{\prime} = 0.478$

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-18 — α range in air) is the form associated with Bragg–Kleeman. Working symbols: $E$ $\rightarrow$ $R$ . Range is the integral of 1/(dE/dx). Alphas of a few MeV stop in centimetres of air.

Purpose

Purpose: compute

R

from

E

in Nuclear physics via

R\approx 0.31\,E^{3/2}\,\mathrm{cm}

R ≈ 0.31 E^{3/2} cm for α in air at STP (E in MeV). Bragg–Kleeman sketch. 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

E = 5.500\,\mathrm{MeV}

, the governing relation

R\approx 0.31\,E^{3/2}\,\mathrm{cm}

yields

R = 4.00\,\mathrm{cm}

. A source, a finite track, a stop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

α energy E5.5 MeV

Outputs

Range in air R4.00 cm

Reading speed

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Narration of this film

A source, a finite track, a stop.

Range is the integral of 1/(dE/dx). Alphas of a few MeV stop in centimetres of air.

Reading speed

Watch on YouTube