Answer to Question #9723 Submitted to "Ask the Experts"

I do not recall having come across a value for the tenth-value layer (TVL) for ²⁰¹Tl photons in concrete, although there may well be a value somewhere in the literature.

As you likely know, ²⁰¹Tl emits multiple gamma rays and x rays with energies ranging from about 10 keV to almost 170 keV. It is possible to calculate a value for the TVL for primary photons for a dose-related quantity such as absorbed dose or exposure by using the following equation:

In equation 1, µ_en,i/? represents the mass energy absorption coefficient of the i^th photon in the dose medium of interest. The i^th photon yield is y_i and its energy is E_i. The quantity µ_i represents the linear attenuation coefficient of the i^th photon in concrete, and T represents the tenth-value layer, considering all the photons, for the dose quantity of interest. I carried out such a calculation for dose or exposure in air, simplifying a bit by assuming a fixed value for µ_en,i/? (in actuality, the value varies from about 0.0241 to 0.0272 cm²g^-1). Values of the photon yields and energies were taken from ICRP Publication 38, Radionuclide Transformations Energy and Intensity of Emissions, International Commission on Radiological Protection, 1983. Values of mass attenuation coefficients for concrete and mass energy absorption coefficients for air can be found by clicking on the material of interest on this NIST page. In doing the calculation, I included nine different photons. I also neglected three photons, which were less than 14 keV in energy (these are all L x rays) since they are attenuated to a degree that they will not contribute noticeably to the estimation.

The form of equation 1 is not amenable to a direct analytical solution for T. It can be solved by various iterative techniques. I used such a technique that was available on a hand-held calculator. I used the mass attenuation coefficients directly rather than converting them to linear attenuation coefficients so the value of T, the tenth-value layer, that I obtained was in density thickness units. The calculated value was 11.9 g cm^-2. If we assume a nominal density of 2.35 g cm^-3 for ordinary concrete, we may convert this density thickness to a linear thickness of about 5.1 cm, which seems like a reasonable value.

If you have the time and resources, you might try doing the calculation yourself to attempt to confirm the value I obtained.

George Chabot, PHD, CHP