Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

INTERACTION OF RADIATION WITH M ATTER 169
where N is the number of absorber atoms per cm 3 . Note that the dimensions of
μa are cm 2 , the units of area. For this reason, the atomic attenuation coefficient is
almost always referred to as the cross section of the absorber. The unit in which the
cross section is specified is the barn, b.
1b= 10 −24 cm 2 .
The atomic attenuation coefficient is also called the microscopic cross section and is
symbolized by σ , while the linear attenuation coefficient is often called the macroscopic
cross section and is given by the symbol . This nomenclature is almost always used
in dealing with neutrons. Equation (5.30) can thus be written as
−1 cm
cm = σ 2 atoms
× N . (5.31)
atom cm3 Using the relationship given in Eq. (5.31), Eq. (5.27) may be rewritten as
I
I0
= e −μat = e −σ Nt . (5.32)
The linear attenuation coefficient for a mixture of materials or an alloy is given by
n
μl = μa1 × N1 + μa2 × N2 +···= μan × Nn, (5.33)
where
n=1
μn = atomic coefficient of the nth element and
Nn = number of atoms per cm 3 of the nth element.
The numerical values for μa have been published for many elements and for a wide
range of quantum energies. * With the aid of atomic cross sections and Eq. (5.33), we
can compute the attenuation coefficients of compounds or alloys containing several
different elements.
W EXAMPLE 5.11
Aluminum bronze, an alloy containing 90% Cu (atomic weight = 63.57) and 10% Al
(atomic weight = 26.98) by weight, has a density of 7.6 g/cm 3 . What are the linear
and mass attenuation coefficients for 0.4-MeV gamma rays if the cross sections for
Cu and Al for this quantum energy are 9.91 and 4.45 b?
Solution
From Eq. (5.33), the linear attenuation coefficient of aluminum bronze is
μl = (μa)Cu × NCu + (μa)Al × NAl.
* Gladys White Groodstein: X-Ray Attenuation Coefficients from 10 KeV to 100 MeV. NBS Circular
583, U.S. Government Printing Office, Washington, DC, 1957.