Physics and Engineering of Radiation Detection

2.4. Interaction of Heavy Charged Particles with Matter 119

apparent that theoretical computation of range is a difficult task. A number of ex-
perimentalists therefore turned to empirical means of measuring this quantity and
modeling the behavior on the basis of their results.
Bragg and Kleeman gave a formula to compute the range of a particle in a medium
if its range is known in another medium.

R 1

R 2

=

ρ 2

ρ 1

[

A 1

A 2

] 1 / 2

(2.4.21)

HereρandArepresent density and atomic mass of the materials. If we have a
compound material an effective atomic mass given by

1

√

Aef f

=

∑

i

wi

√

Ai

, (2.4.22)

is used instead. Herewiis the weight fraction ofithelement having atomic massAi.

E.1 Range ofα-Particles

Several empirical and semi-empirical formulae have been proposed to compute range
ofα-particles in air. For example, (56),

Rairα [mm]=

⎧

⎪⎨

⎪⎩

e^1.^61

√

Eα forEα< 4 MeV

(0. 05 Eα+2.85)Eα^3 /^2 for 4MeV≤Eα≤ 15 MeV

(2.4.23)

and

Rairα [cm]=

⎧

⎪⎨

⎪⎩

0. 56 Eα forEα< 4 MeV

1. 24 Eα− 2 .62 for 4MeV≤Eα< 8 MeV

(2.4.24)

Both of these equations yield almost same results as can be seen from Fig.2.4.7
which has been plotted for theα-particles having energy up to 8MeV. Hence at
least in this energy range one could use any one of these equations to compute the
range in air. To compute the range in some other material, equation 2.4.21 can be
used. For example, at normal pressure and temperature the range ofα-particles in
any materialxcan be determined from

Rxα=3. 37 × 10 −^4 Rairα

√

Ax

ρx

. (2.4.25)

Here we have used the effective atomic number of airAair=14.6anditsdensity
ρair=1. 29 × 10 −^3 g/cm^3. Although it is very tempting to use Bragg-Kleeman rule,
however it should be noted that the values thus obtained are only approximations
and care must be taken while using them to draw conclusions.