Answer to Question #3890 Submitted to "Ask the Experts"

What is the density and the linear attenuation coefficient (at the ¹³⁷Cs energy) of common 8" cinder blocks?

Unfortunately, there is not a single, well-defined answer to your question. "Common" cinder blocks are made of concrete and come in more than one internal geometry. Blocks with nominal dimensions of 8" x 8" x 16" (the finished external dimensions are commonly about 7.5" x 7.5" x 15.5") may be either solid or may be partially hollow. A common partially hollow variety has two cavities, each about 5" x 5" x 8", that extend through the nominal 8" depth and are situated symmetrically along the length of the block. The nominal 8" x 16" side walls of the block are solid concrete, each about 1.25" to 1.5" thick where they bound the cavities. There are other variations of the cinder block, one other being a block with three separate cavities, each about 3" x 5" in cross section extending through the thickness of the block. In some cases the cavities are not really rectangular parallelepipeds but may have more oval cross sections.

The point of saying all this is to make clear the fact that the attenuating properties of "cinder blocks" may differ noticeably among themselves, depending on the physical characteristics of the blocks. What can be said is that the blocks are usually made of ordinary concrete with a likely mass density between 2.2 and 2.4 grams per cubic centimeter. For a density of 2.3 g/cm³ the expected linear attenuation coefficient for the concrete at the ¹³⁷Cs photon energy (662 keV) would be about 0.181 per centimeter. Values for the mass attenuation coefficients for concrete as a function of photon energy may be obtained from several sources, one convenient one being the National Institute of Standards and Technology Web site. The mass attenuation coefficients may be converted to linear coefficients by multiplying by the mass density of the concrete.

The transmission factor for ¹³⁷Cs photons incident normally on the block would be given by e^-µX, where e is the base of the natural logarithm (2.718), µ is the linear attenuation coefficient, and X is the thickness of the concrete. For a solid block 7.5" (19 cm) thick the transmission factor would be e^-(0.181)(19) = 0.0321. For the two-cavity block described above, with 1.25" (3.18 cm) thick side walls, the transmission factor for the concrete walls bounding a cavity would be e^{-(0.181)(2)(3.18)} = 0.316. Thus, the solid block would be about 10 times more effective than the hollow block in attenuating the primary photons. If you know the physical characteristics of the cinder blocks you are dealing with you should be able to make a reasonable estimate of their attenuating properties. Note that the attenuating ability of a given partially hollow block will vary over the surface of the block because of changes in the concrete thickness especially near the ends and midlength of the (two cavity) block where the concrete extends through the entire depth of the block. Note also that the above transmission example applies only to the primary photons. In actual situations you may also have to consider the presence of scattered photons produced by Compton events in the concrete; some of these will contribute to photons and dose at the outer surface of the concrete.

George Chabot, PhD, CHP