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 ?

  • A 𝑥 = 𝜇 ( 2 ) l n
  • B 𝑥 = 1 𝜇
  • C 𝑥 = 2 𝜇
  • D 𝑥 = ( 2 ) 𝜇 l n
  • E 𝑥 = ( 2 ) 𝜇 l n

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.

  • A 1 . 3 1 × 1 0 cm2/g
  • B 1 . 3 1 × 1 0 cm2/g
  • C 76.4 cm2/g
  • D 16.7 cm2/g
  • E 1.67 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 . 4 1 × 1 0 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 ?

  • A 𝜇 = 𝜇 𝜌
  • B 𝜇 = 𝜇 𝜌
  • C 𝜇 = 𝜇 𝜌
  • D 𝜇 = 𝜇 ( 2 ) 𝜌 l n
  • E 𝜇 = 𝜌 𝜇

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 . 5 2 × 1 0 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 . 7 9 𝐼 . What is the half-thickness of the material? Give your answer to 2 significant figures.

  • A 9.5 cm
  • B 35 cm
  • C 60 cm
  • D 2.8 cm
  • E 6.0 cm

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