CAIE A-Level Physics A2 24.2 Production and Use of X Rays Questions

Practise analysing X-ray production, minimum wavelength, attenuation, image contrast and CT reconstruction, including radiation exposure comparisons.

Exam points

explain X-ray production and calculate minimum wavelength from accelerating p.d.
interpret X-ray image contrast from material attenuation and transmitted intensity
calculate X-ray transmission or absorption using I = I?e??x
explain CT reconstruction from multiple angled images and sections
evaluate CT against single X-ray imaging, including 3D information and radiation exposure

Covered syllabus points

24.2.1—That X-rays are produced by electron bombardment of a metal target and 24.2.2—The use of X-rays in imaging internal body structures 24.2.3—I = I0e–µx for the attenuation of X-rays in matter 24.2.4—Computed tomography (CT) scanning produces a 3D image of an internal

[Maximum number: 10]

(a)

Electrons are accelerated through a potential difference of 15 kV . The electrons collide with a metal target and a spectrum of X-rays is produced.

[ 5 ]

(i)

Explain why a continuous spectrum of energies of X-ray photons is produced.

[ 3 ]

(ii)

Calculate the wavelength of the highest energy X-ray photon produced.

[ 2 ]

$e V=\frac{h c}{\lambda}$ $\lambda=\frac{6.63 \times 10^{-34} \times 3.0 \times 10^{8}}{1.6 \times 10^{-19} \times 15000}$ $=8.3 \times 10^{-11} \mathrm{~m}$
or

E=h f and $c=f \lambda$ and electron energy =eV

or

$E=h c / \lambda$ and electron energy =eV
$\begin{aligned} \text { electron energy } & =1.6 \times 10^{-19} \times 15000 & =2.4 \times 10^{-15} \end{aligned}$ $\lambda=\frac{6.63 \times 10^{-34} \times 3.0 \times 10^{8}}{2.4 \times 10^{-15}}$ $\lambda=8.3 \times 10^{-11} \mathrm{~m}$

(b)

A beam of X-rays has an initial intensity $I_{0}$ . The beam is directed into some body tissue. After passing through a thickness x of tissue the intensity is I. The graph in Fig. 11.1 shows the variation with x of $\ln \left(I / I_{\mathrm{o}}\right)$ .

Fig. 11.1

[ 5 ]

(i)

Determine the linear attenuation (absorption) coefficient $\mu$ for this beam of X-rays in the tissue.

\mu=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \ldots . . . . . . . . . . . . . . . . . . . . . ~ \mathrm{~cm}^{-1}

[ 3 ]

$\mu=-$ gradient or $\ln \left(I / I_{\mathrm{o}}\right)=-\mu x$
(e.g. 2.08 / 10.0) $=\mathbf{0 . 2 1} \mathrm{cm}^{-1}$

(ii)

Determine the thickness of tissue that the X-ray beam must pass through so that the intensity of the beam is reduced to 5.0 % of its initial value. cm

[ 2 ]

$\ln (0.05)=-\mu x$ $x=\frac{\ln 0.05}{-\mu}$

e.g. $x=14 \mathrm{~cm}$

[Maximum number: 3]

(a)

State what is meant by contrast in an X-ray image.

[ 1 ]

(b)

A parallel beam of X-ray radiation is incident, separately, on samples of bone and of muscle.

Data for the thickness x of the samples of bone and of muscle, together with the linear attenuation coefficients $\mu$ of the radiation in bone and in muscle, are given in Table 10.1.

Table 10.1

Calculate the ratio
> intensity of radiation transmitted through the bone
> intensity of radiation transmitted through the muscle ⋅

ratio =

[ 2 ]

$I=I_{0} \exp (-\mu x)$
ratio $=(\exp \{-1.5 \times 2.9\}) /(\exp \{-4.0 \times 0.95\})(=\exp \{-0.55\})$

ratio = 0.58

[Maximum number: 7]

(a)

Electrons in a vacuum are accelerated through a potential difference of 84 kV . The electrons then strike a metal target and X-rays are produced.

[ 4 ]

(i)

Calculate the minimum wavelength of the X-rays that are produced.
wavelength = m

[ 2 ]

$e V=h c / \lambda$ $\begin{aligned} \lambda =\left(6.63 \times 10^{-34} \times 3.00 \times 10^{8}\right) /\left(84 \times 10^{3} \times 1.60 \times 10^{-19}\right) =1.5 \times 10^{-11} \mathrm{~m} \end{aligned}$

(ii)

The melting points of two metals are given in Table 9.1.

Table 9.1

Suggest why the metal target is made from tungsten rather than copper.

[ 2 ]

(b)

An X-ray beam is incident normally on a sample of soft tissue and bone as shown in Fig. 9.1.

Fig. 9.1

Data for the two materials are given in Table 9.2.

Table 9.2

The total thickness of soft tissue is x. The total thickness of bone is also x.
The incident intensity of the X-ray beam is $I_{0}$ . The transmitted intensity of the X-ray beam is 13 % of the incident intensity.

Determine x, in cm .

[ 3 ]

$I=I_{0} \exp (-\mu t)$ $0.13=[\exp (-3.0 x)] \times[\exp (-0.22 x)]$
= exp (-3.22x)
$x=0.63 \mathrm{~cm}$

[Maximum number: 1]

State what is meant by contrast in an X-ray image.

[Maximum number: 3]

An X-ray beam is incident normally on a sample of soft tissue and bone as shown in Fig. 9.1.

Fig. 9.1

Data for the two materials are given in Table 9.2.

Table 9.2

$I=I_{0} \exp (-\mu t)$ $0.13=[\exp (-3.0 x)] \times[\exp (-0.22 x)]$
= exp (-3.22x)
$x=0.63 \mathrm{~cm}$

[Maximum number: 2]

In medical diagnosis, X-rays may be used to produce a single X-ray image or may be used in computed tomography (CT scanning).

Suggest an advantage and a disadvantage of CT scanning compared with single X-ray imaging for diagnosis.
advantage:
disadvantage:

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question 2

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Question (b)

Question 3

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Question (i)

Question (ii)

Question (b)

Question 4

Question 5

Question 6