(ii) Thickness of the absorbing material also called as half-value layer is defined as
x H ¼
0:693
l
Solved Examples
Example 1 Calculate the percentage of intensity of the X-ray that will pass
through 0.005 m thick of an aluminum sheet. The linear attenuation coefficient for
aluminum for K a line emitted by a tungsten target in is 139 m
À1 .
Solution: Given: l ¼ 139m
À1
; thickness x = 0.005 m, percentage of transmitted
intensity = ?
Let X% of the intensity is being transmitted through the aluminum sheet, then
we have
X% ¼
I
I 0
or
X
100
¼ exp Àlx
ð
Þ
or
X ¼ 100 exp Àlx
ð
Þ
¼ 100 exp À139 Â 0:005
ð
Þ ¼50%
Example 2 Determine the attenuation percentage in an X-ray beam after passing
through a thickness of a material equal to four-half value thickness.
Solution: Given: x = 4x H , attenuation % = ?
We know that the attenuation coefficient in terms of half value layer is given by
l ¼
0:693
x H
or l x H ¼ 0:693
Now, let the attenuation in the intensity of X-ray after passing through a
thickness of material is X%, therefore
I
I 0
¼ 100 À X
ð
Þ % ¼
100 À x
100
¼ 1 À
X
100
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7 Diffraction of Waves and Particles by Crystal