Question 32.WE.1: The attenuation (absorption) coefficient of bone is 600 m^−1...

Cambridge International AS and A Level Physics Coursebook

The attenuation (absorption) coefficient of bone is $600 m^{−1}$ for X-rays of energy 20 keV. A beam of such X-rays has an intensity of $20 Wm^{−2}$ . Calculate the intensity of the beam after passing through a 4.0 mm thickness of bone

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

Step 1 Write down the quantities that you are given; make sure that the units are consistent.
$I_{0} = 20 Wm^{−2}$
x = 4.0 mm = 0.004 m
$µ = 600 m^{−1}$
Step 2 Substitute in the equation for intensity and solve.
Hint: Calculate the exponent (the value of –µx) first.
$I = I_{0} e^{−µx}$

= 20 × e^{−(600  ×  0.04)} = 20 × e^{−2.4}

$= 1.8 Wm^{−2}$
So the intensity of the X-ray beam will have been reduced to about 10% of its initial value after passing through just 4.0mm of bone.

Related Answered Questions

Question: 32.WE.2

A beam of ultrasound is normally incident on the boundary between muscle and bone. Use Table 32.3 to determine the fraction of its intensity which is reflected. ...

Verified Answer:

Step 1 Write down the values of

Z_{1}[/late...

Question: 32.11

Quartz is an example of a piezo-electric material. The speed of sound in quartz is 5700 m s^−1. a Calculate the wavelength of ultrasound waves of frequency 2.1 MHz in a quartz crystal. b If the crystal is to be used in an ultrasound transducer, its thickness must be half a wavelength. Calculate the ...

Verified Answer:

a Rearrange speed v = fλ to give wavelength [latex...

Question: 32.7

The data in Table 32.2 shows how the attenuation coefficient μ depends on the energy of the X-rays in bone and muscle. When making a diagnostic X-ray image, it is desirable that bone should be clearly distinguished from muscle. Use the data in Table 32.2 to explain why it would be best to use lower ...

Verified Answer:

Consider the ratio of attenuation coefficients bon...

Question: 32.2

Determine the minimum wavelength of X-rays emitted from an X-ray tube operated at a voltage of 120 kV. ...

Verified Answer:

Photon energy

E = \frac{hc}{λ} = V × e[/lat...

Question: 32.21

An MRI scan might be considered a safer procedure than a CT scan. a Explain why it might be considered to be safer. b Why might a CT scan be chosen in preference to an MRI scan? c Explain why MRI is described as non-invasive ...

Verified Answer:

a MRI uses non-ionising RF electromagnetic radiati...

Question: 32.20

Figure 32.33 shows how the amplitude of RF waves coming from watery tissue varies after resonance. Copy the graph and add lines and labels to show the graphs you would expect to see for cancerous and fatty tissues. ...

Verified Answer:

Question: 32.19

Protons precess at a frequency of 42.6 MHz in an external field of magnetic flux density 1.0 T. a Determine the frequency at which will they precess in a field of magnetic flux density 2.5 T. b State the frequency of RF radiation that will cause the protons to resonate in this stronger magnetic ...

Verified Answer:

a Rearrange

f_{0} = \frac{γB_{0}}{2π}[/late...

Question: 32.18

Explain why an ultrasound B-scan, rather than X-rays, is used to examine a fetus. ...

Verified Answer:

X-rays are ionising radiation and hence are damagi...

Question: 32.17

Two consecutive peaks in an ultrasound A-scan are separated by a time interval of 0.034 ms. Calculate the distance between the two reflecting surfaces. (Assume that the speed of sound in the tissue between the two surfaces is 1540 m s^−1.) ...

Verified Answer:

Distance

= \frac{cΔt}{2} = \frac{1540 × 0...

Question: 32.WE.3

In a particular A-scan, similar to Figure 32.26, the time interval between pulses 1 and 2 is 12 µs. The speed of ultrasound in bone is about 4000 m s^−1. Determine the thickness of the bone. ...

Verified Answer:

Step 1 Determine the distance travelled by the ult...