100 Chapter 2. Interaction of Radiation with Matter
Therefore usingI=I 010 −^4 in equation 2.3.33 we can determine the required
thicknessdas follows.I = I 0 e−μtd
10 −^4 = e−μtd
⇒ ln(10−^4 )=−μtd⇒ d =−ln(10−^4 )
μtThe total linear attenuation coefficient can be determined from the given mass
attenuation coefficient using relation 2.3.36.μt = μmρ
= 122. 8 × 11 .3 = 1387. 64 cm−^1Hence the required thicknessdof lead isd = −ln(10−^4 )
μt= −ln(10−^4 )
1387. 64
=0. 0066 cm=66μm.This result clearly shows the effectiveness of lead in attenuating photons.
Lead is commonly used for shielding purposes in radiation environments.Let us now see how the attenuation coefficient for a particular material can be
determined. Since there is direct relation between attenuation coefficient and the
cross section therefore if we know the total cross section, we can determine the total
attenuation coefficient. The total cross sectionσtcan be determined by simply
adding the cross sections for individual processes, that is
σt=σpe+σc+σry+σpair+σtrip+....., (2.3.40)where the subscriptspe,c,ry,pair,andtriprepresent the photoelectric effect,
Compton scattering, Rayleigh scattering, pair production, and triplet production
respectively. The dots represent other processes such as Thompson scattering and
photonuclear interactions. Then, according to equations 2.3.38 and 2.3.39, the total
linear and the total mass attenuation coefficients can be determined from
μt=ρNA
A(σpe+σc+σry+σpair+σtrip+.....) (2.3.41)μm=NA
A
(σpe+σc+σry+σpair+σtrip+.....). (2.3.42)The tabulated values of photon attenuation coefficients found in literature are actu-
ally computed using this method. However, since such computations depend heavily
on theoretically obtained formulas for cross sections, therefore sometimes it is de-
sired that the coefficients are also experimentally measured. Discrepancies of around
5% between theoretical and experimental values are not uncommon.