Physics and Engineering of Radiation Detection

142 Chapter 2. Interaction of Radiation with Matter

Example:

Compute the thickness of a gold foil needed to remove 90% of the neutrons

from a beam of thermal neutrons. The total cross section of thermal neutrons

in gold can be taken to be 100b. The density of gold is 1. 9 × 104 kgm−^3.

Solution:

The attenuation coefficient of thermal neutrons in gold is

μn =

NAρ

A

σt

=

(

6. 022 × 1023

)(

1. 9 × 104

)

197 × 10 −^3

100 × 10 −^28

= 580. 8 m−^1.

Note that here we have usedAinkg/mole. To compute the thickness of the

foil we can use equation 2.6.12. For 90% removal of the neutrons we substitute

I/I 0 =0.1andμnas calculated above in this equation to get

x =

1

μn

ln

(

I 0

I

)

=

1

580. 8

ln(10)

=3. 96 × 10 −^3 m=3. 96 mm.