Saturday, June 7, 2014

nuclear engineering - X-ray shielding



X-ray shielding, why is lead used to shield us when taking X-ray images?


As far as I remember (but can't find it on wikipedia ... ), the deflection on (high energy) photons increases the more heavier the nuclei are. (Don't remember and don't find if it's really the mass or rather the proton number.)


In either case, there are heavier, more dense materials with higher proton numbers.


The material is not consumed nor altered by exposure to X-rays. So why don't we use gold or depleted uranium (just to name some alternatives)?


(Not sure about tags, if anyone knows better, please feel free to suggest/add some others.)


Edit: as the answers and comments here helped me to clear my mind to change the question, but the new question is sufficiently different, I've asked a follow-up here: Formula for scattering and energy change of photons on (naked) nuclei



Answer



I pulled out my notes from a shielding class and found that the absorption cross section per atom follows a rule: $$\sigma_a\sim\frac{Z^p}{E^3},$$ where $z$ is the atomic number of the absorber atom, $E$ is the energy of the photon, and $p$ is an energy dependent value between 3 and 5. For most x-rays, $p\simeq 4$.


While the cross-section per atom does indeed get larger for increasing $Z$, the density of the material is important, too. The density peaks at osmium ($Z=76$), then drops off, then climbs again in the actinides, but never reaches densities near osmium and iridium ($Z=77$).


When considering the effectiveness of an shield/absorber, one must consider the combined effects of cross-section per atom and density. The result of this is a quantity known as the linear attenuation coefficient, $\mu$, which is typically quoted in $\mathrm{cm}^{-1}$. This is used to calculated the intensity of radiation after travelling through a thickness, $x$ of a material: $$I(x)=I_0 e^{-\mu x}.$$



A quick search of the internet turned up a compilation of x-ray absorption coefficients called the McMaster Tables.


Medical and dental x-rays fall in the energy realm of $5-150\ \mathrm{keV}$. Mammography x-rays use a filtered $20\ \mathrm{keV}$ discrete x-ray from a Mo anode, so I chose to compare linear absorption coefficients at $20\ \mathrm{keV}$ for several elements:


Element  Z   linear atten. (1/cm) @ 20 keV  density (g/cm3)
W 74 1293 19.3
Re 75 1446 21.0
Os 76 1585 22.5
Ir 77 1648 22.4
Pt 78 1629 21.4
Au 79 1515 19.4
Pb 82 975 11.3

Th 90 1152 11.7
U 92 1307 19.1

All these will, in general, smoothly scale up for lower energy and scale down for higher energy except when a binding energy edge of a K, L, or M shell electron falls at that energy. Then there will be a sharp spike upward.


One must also keep in mind that absorption is followed by a follow-up (lower energy) x-ray because the absorption displaces an electron from an atom, and that hole must be filled. In designing a shield you need to know the incoming energies and the consequential energies that follow the absorption. That's why low-background shields for low-energy gamma and x-ray counting systems use lead, lined with cadmium, then lined with copper.


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