Attenuation of X-rays

A 3D printer can manufacture small objects.

Some 3D printers use polylactic acid (PLA). PLA is supplied in the form of long filaments. The 3D printer melts the PLA and builds up the shape of the desired object in layers.

The electrical supply to the heater in the printer has an e.m.f., , of 12 V. The power of the heater is 40 W.

Calculate the resistance, R, of the heater.

The specific latent heat of fusion of PLA is 9.4 × 10⁴ J kg^–1 and its melting point is 160 °C. (b)

Define specific latent heat of fusion.

Calculate the maximum mass m of PLA that the heater could melt in one minute.

Explain why the printing process is slower in practice than your answer to (ii) suggests.

High-energy X-ray photons can destroy living cells. In radiotherapy, these photons are targeted at cancer cells.

The radiation dose is the amount of energy that a patient’s body absorbs from the high-energy X-ray photons.

Fig. 6.2 shows how this dose changes with depth below the surface of the skin.

The dose initially rises with depth because the high-energy X-ray photons produce electrons and positrons as they pass through the body. These electrons and positrons are quickly absorbed, increasing the dose.

Explain why high-energy X-ray photons produce electrons and positrons as they pass through the body.

*(ii) A 3D object called a bolus is used in radiotherapy for patients with skin cancer. A bolus targets the maximum radiation dose near the surface of the skin. So using a bolus makes the radiotherapy more effective.

A bolus can be made from PLA using a 3D printer. The bolus must fit the shape of the patient’s body exactly. This shape is found beforehand by giving the patient either a CAT scan or a PET scan.

• Explain how CAT scans and PET scans work.

• Discuss the advantages and disadvantages of having a scan to produce a bolus for radiotherapy.

Describe, in terms of X-ray photons, the attenuation mechanism of Compton scattering.

Use the graph to determine the exposure time t for the total radiant energy incident per cm² at a depth of 1.0 cm to be 2.6 J.

Beyond x = 1.0 cm, the tissue has a larger attenuation coefficient than the value calculated in (i).

On Fig. 24.2, sketch the variation of I with x beyond x = 1.0 cm.

A high-energy X-ray photon interacts with an electron of an atom through the Compton effect.

Describe this effect.

The diagram below shows a beam of X-rays incident normally on some soft tissue.

The attenuation (absorption) constant of the soft tissue is 0.85 cm^–1. The intensity of the beam is 4.6 × 10³ W m^–2. There is a small cyst 2.1 cm from the surface of the soft tissue. The cross-sectional area of the cyst normal to the beam is 3.4 × 10^–4 m².

The beam is switched on for 30 s.

Calculate the X-ray energy incident on the cyst in a period of 30 s.

The attenuation coefficients of the cyst and the soft tissues in (b) were similar. This prevented imaging the cyst using a two-dimensional X-ray image.

Name a different X-ray technique that could be used to image the cyst. Explain the advantage of this technique.

X-ray photons interact with atoms.

The attenuation coefficient against lg(photon energy) graphs for simple scattering (S), photoelectric effect (PE), Compton effect (C) and pair production (PP) are shown below.

With the help of a calculation, explain the minimum photon energy shown on the graph for pair production.

The intensity of a beam of X-rays incident on material P is I₀. The beam passes through 0.50 cm of material P and 0.50 cm of material Q.

The absorption (attenuation) coefficients of P and Q are 0.60 cm^–1 and 0.20 cm^–1 respectively. The intensity of the beam after passing through both P and Q is n I₀.

What is the value of n ?

A 0.67

B 0.74

C 0.82

D 0.90

Your answer

Describe the basic structure of an X-ray tube and explain how X-ray photons are produced. You may draw a labelled diagram.

A beam of X-rays is directed at tissues in a patient. The X-ray photons interact with the atoms of the tissues.

Simple scatter is one of the attenuation mechanisms.

Name and describe two other attenuation mechanisms.

There are four important attenuation mechanisms by which X-ray photons may interact when they pass through matter.

In which mechanism is the X-ray photon scattered with a longer wavelength?

A simple scattering

B Compton effect

C pair production

D photoelectric effect

Your answer