Question 2.11: Boron is frequently used as a material to shield against the......
Boron is frequently used as a material to shield against thermal neutrons. Using the data in Appendix E Estimate the thickness of boron required to reduce the intensity of a neutron beam by a factors 100, 1,000, 10,000 and 100,000.
Since the scattering cross section of boron is only 4.27 b while the absorption cross section is 767 barns. We will assume that it is a pure absorber. Its density is 2.45 gm/cm³. Thus \Sigma={\frac{\rho N_{o}}{A}}\sigma={\frac{2.45\cdot0.6023\cdot10^{24}}{10.82}}\cdot767\cdot10^{-24}=105\;c m^{-1}. Let a be the attenuation factor. Thus 1/a=\exp(-\Sigma x){\mathrm{~~or~}}x=-\ln(1/a)/\Sigma=\ln(a)/\Sigma\,.Thus
x=\ln(a)/\Sigma=\ln(100)/10{5}=0.044 cm
x=\ln(a)/\Sigma=\ln(1000)/10{5}=0.065 cm
x=\ln(a)/\Sigma=\ln(10000)/10{5}=0.088 cm
x=\ln(a)/\Sigma=\ln(100000)/10{5}=0.110 cm