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Question 2.1: Neutrons impinge on a material with a cross section of Σ = 0......

Neutrons impinge on a material with a cross section of Σ = 0.8\text{ cm} ^{-1} . How thick must the material be if no more than 5.0% of the neutrons are to penetrate the material without making a collision? What fraction of the neutrons make their first collision within the first 2.0 cm. of the material?

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From Eq. (2.4) 0.05 = 1.0 exp(−0.8x) or x = −ln(0.05) / 0.8 = 3.74 cm
The fraction colliding is just 1- fraction penetrating without making a collision. Thus 1 − exp(−0.8 · 2.0) = 0.798

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