Question 5
(a)
An X-ray source is placed on one side of a metal plate, as shown in
Fig. 11.1.
Fig. 11.1
The intensity of the
X-ray beam is measured at points A and B.
State two reasons,
other than absorption of X-ray photons in the metal, for the intensity at point
A to be different to that at point B. [2]
(b)
A specimen of muscle and bone undergoes X-ray examination. Parallel
beams of X-rays are incident on the specimen, as shown in Fig. 11.2.
Fig. 11.2
The specimen has a
total thickness of 4.0 cm. One section contains a bone of thickness
1.5 cm.
Data for the linear
absorption (attenuation) coefficient μ for
the bone and for the muscle in the specimen are given in Fig. 11.3.
μ /
cm-1
bone 3.0
muscle 0.27
Fig. 11.3
(i)
Calculate the ratio
intensity of X-ray beam incident on the
specimen .
intensity of X-ray beam emerging from the specimen
for the beam passing
through
1.
the 4.0 cm thickness of muscle alone, [2]
2.
the bone and the muscle. [2]
(ii)
Using your answers in (i), suggest and explain
whether an X-ray image of this specimen is likely to have good contrast. [2]
Reference: Past Exam Paper – November 2015 Paper 43 Q11
Solution:
(a)
e.g.
scattering
{of the X-ray beam} (in the metal)
the beam
is not parallel (not just “A closer than B”)
reflection
(from metal)
diffraction
in the metal/lattice
(b)
(i)
1.
{I = I0
exp(-μx)
Ratio = I0
/ I
I / I0
= exp(-μx)
So, I0
/ I = exp(μx)
Ratio =
exp(μx) }
ratio = exp(μx)
ratio =
exp(0.27 × 4.0)
ratio =
2.94 (2.9)
2.
{The beam
passes through 1.5 cm of bone and (4.0 – 1.5 =) 2.5 cm of mucle. As the beam
passes through each of them, it gets attenuated.
ratio = exp(μx)
Through
2.5 cm muscle only: ratio = exp(0.27×2.5) = 1.96
Through 1.5
cm bone only: ratio = exp(3.0×1.5) = 90
To obtain
the overall ratio for the beam going through both the muscle and bone, we
multiply the 2 ratios.}
ratio =
exp(0.27 × 2.5) × exp(3.0 × 1.5)
ratio =
1.96 × 90
ratio =
177 (180)
(ii)
Each ratio
gives a measure of the transmission {of the beam}.
Since the ratios (in (i)) are very different, the
image will have a good contrast.
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