Thermal neutrons are captured by the 10^18 atoms/cm^3 of chromium on the bumpers

Question

Thermal neutrons are captured by the 10^18 atoms/cm^3 of chromium on the bumpers of a '54 Chevy. The chromium has 'natural' isotopic abundances, but only two of the chromium isotopes have significant neutron capture cross-sections: ^50 Cr (4.3% abundance, 15.8b cross-section) and ^53 Cr (9.5% abundance, 18b). a. What are the number densities of the ^53 Cr and the ^50 Cr? b. What is the 'macroscopic cross section' for neutron capture by the ^53 Cr? c. What fraction of the neutrons are captured by the ^50 Cr?

Explanation / Answer

a) No. density of Cr53=4.3/100*1018=4.3*1016 atoms/cm3

No.density of Cr50=9.5/100*1018=9.5*1016 atoms/cm3

b) Macroscopic cross section for neutron capture by the Cr53=No.of Cr53 atoms/m3* Volume of bumper *cross section of neutron capture per Cr53 atom=4.3*1016 *106*18*10-28*V =7.7*10-5V where V=Area *thickness of bumper

c) Fraction of neutrons captured by the Cr50=Macroscopic cross section/Area of bumper=9.5*1016*106*15.8*10-28V/Area of bumper=1.5*10-4*thickness of bumper

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