Question 2.3: A material has a neutron cross section of 3.50 × 10^−24 cm²/......
A material has a neutron cross section of 3.50 \times 10^{-24} cm²/nuclei, and contains 4.20 \times 10^{23} nuclei/cm³:
a. What is the macroscopic cross section?
b. What is the mean free path?
c. If neutrons impinge perpendicularly on a slab of the material, which is 3.0 cm thick, what fraction of them will penetrate the slab without making a collision?
d. What fraction of the neutrons in part c will collide in the slab before penetrating a distance of 1.5 cm ?
\sigma=3.5 \cdot 10^{-24} \;cm^2 \quad \quad N^{\prime \prime \prime}=4.2 \cdot 10^{23} \,/\,cm^3
a. \quad \Sigma=\sigma N^{\prime \prime \prime}=3.5 \cdot 10^{-24} \cdot 4.2 \cdot 10^{23}=1.47 \;cm ^{-1}
b. \quad \lambda=1 / \Sigma=0.68 \;cm
c. \quad\exp (-\Sigma \cdot 3)=\exp (-1.47 \cdot 3)=0.0122
d. \quad 1-\exp (-\Sigma \cdot 1.5)=1-\exp (-1.47 \cdot 1.5)=0.890