Worksheet: Attenuation of Electromagnetic Radiation in Solid Materials

In this worksheet, we will practice calculating the proportion of electromagnetic radiation that remains when the radiation passes through a solid barrier.

Q1:

Which of the following formulas correctly relates the half-thickness of a material, 𝑥, to its linear attenuation coefficient, 𝜇?

  • A𝑥=(2)𝜇ln
  • B𝑥=2𝜇
  • C𝑥=1𝜇
  • D𝑥=(2)𝜇ln
  • E𝑥=𝜇(2)ln

Q2:

A beam of X-rays is directed toward a thick gold sheet. Each X-ray photon in the beam has an energy of 2.21 keV, and the half-thickness of gold for 2.21 keV photons is 0.391 cm. What is the intensity of the beam, as a ratio of the initial intensity, once it has passed through 0.8 cm of the gold sheet? Give your answer to 3 significant figures.

Q3:

Lead has a density of 11.3 g/cm3. The linear attenuation coefficient for lead is 0.148 cm−1 for 10 keV X-rays. What is the mass attenuation coefficient for lead for 10 keV X-rays? Give your answer to 3 significant figures.

  • A1.31×10 cm2/g
  • B16.7 cm2/g
  • C76.4 cm2/g
  • D1.31×10 cm2/g
  • E1.67 cm2/g

Q4:

Chromium has a density of 7,190 kg/m3. The mass attenuation coefficient for chromium for 1 keV X-rays is 7.41×10 cm2/g. What is the linear attenuation coefficient of chromium for 1 keV X-rays? Give your answer to 3 significant figures.

Q5:

Zinc has a density of 7.14 g/cm3. The mass attenuation coefficient for zinc for 100 keV X-rays is 0.497 cm2/g. What is the linear attenuation coefficient of zinc for 100 keV X-rays? Give your answer to 3 significant figures.

Q6:

Which of the following formulas correctly relates the mass attenuation coefficient of a material, 𝜇, to its linear attenuation coefficient, 𝜇, and its density, 𝜌?

  • A𝜇=𝜌𝜇
  • B𝜇=𝜇𝜌
  • C𝜇=𝜇𝜌
  • D𝜇=𝜇(2)𝜌ln
  • E𝜇=𝜇𝜌

Q7:

A beam of monoenergetic X-rays passes through two thick sheets of metal. The first sheet of metal is 2.0 cm thick and has a half-thickness of 4.7 cm. The second sheet of metal is 1.3 cm thick and has a half-thickness of 1.5 cm. What is the intensity of the beam, as a ratio of the initial intensity, once it has passed through both sheets of metal? Give your answer to 2 significant figures.

Q8:

A beam of X-rays is directed toward a thick metal sheet. Each X-ray photon in the beam has an energy of 40 keV, and the linear attenuation coefficient of the metal for 40 keV photons is 0.23 cm−1. What is the intensity of the beam, as a ratio of the initial intensity, once it has passed through 10 cm of the material? Give your answer to 2 significant figures.

Q9:

A beam of gamma rays is directed toward a block of concrete that is 2.4 m thick. Each gamma-ray photon has an energy of 3.0 MeV. On the far side of the concrete block, the intensity of the beam is found to have reduced to 5.52×10 of its initial intensity.

What is the linear attenuation coefficient for 3.0 MeV photons in concrete? Give your answer to 2 significant figures.

Concrete has a density of 2.4 g/cm3. What is the mass attenuation coefficient for 3.0 MeV photons in concrete? Give your answer to 2 significant figures.

Q10:

A beam of monoenergetic X-rays passes through a sheet of material that is 12 cm thick. The intensity of the beam once it has passed through the sheet of material is equal to 0.79𝐼. What is the half-thickness of the material? Give your answer to 2 significant figures.

Q11:

Zirconium has a half-thickness of 253 nm for photons with an energy of 1.00 keV. What is the linear attenuation coefficient of zirconium for photons of this energy? Give your answer to 3 significant figures.

  • A253 nm−1
  • B2.74×10 cm−1
  • C365 cm−1
  • D2.74×10 nm−1
  • E365 nm−1

Q12:

Rubidium has a linear attenuation coefficient of 7.53 cm−1 for photons with an energy of 50.0 keV. What is the half-thickness of rubidium for photons of this energy? Give your answer to 3 significant figures.

Q13:

The table shows the mass attenuation coefficients for 20.0 keV photons of different materials. Which of the materials shown is the most effective at blocking 20.0 keV photons?

MaterialIronCobaltNickelCopper
Mass Attenuation Coefficient for 20.0 keV Photons (cm2/g)25.728.032.233.8
  • AIron
  • BCopper
  • CNickel
  • DCobalt

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