Homework Set 3 Solutions

# Homework Set 3 Solutions - Homework 24 Solutions Due Friday...

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Homework 24 Solutions Due: Friday 4/9 You are given a bare spherical fast reactor of pure fissile material. a. By equating the geometrical buckling to the material buckling, derive expressions for: i. The critical radius ii. The critical volume iii. The critical mass b. Calculate these values for a U 235 spherical reactor with the following parameters: σ tr = 8.246 b a = 2.844 b ρ = 18.75 g cm 3 νσ f = 5.297 neutron b Compare your result to the actual critical mass of the Godiva Experiment composed of 93.9 % enriched U 235 where M critical = 48.8 kg c. Calculate these values for a Pu 239 spherical reactor with the following parameters: tr = 6.8 b c = 0.26 b = 19.74 g cm 3 ν = 2.98 neutrons f = 1.85 b Compare your result to the actual critical mass of the Jezebel Experiment composed of pure Pu 239 where M critical = 20.53 kg d. Discuss the criticality situation for a sphere made out of U 238 with the following data: tr = 6.9 b c = 0.16 b = 19.05 g cm 3 = 2.6 neutrons f = 0.095 b Discuss the results of your calculations for the attainable critical masses for these materials. a. Start by equating expressions for geometric and material buckling B g 2 = B m 2 π R c 2 = k 1 L 2 R c = L 1 R c = L k 1 V c = 4 3 R c 3 = 4 3 L 1 3 = 4 4 L 3 3 k 1 ( ) 3 2 V c = 4 4 L 3 3 k 1 ( ) 3 2 M c = V c = 4 4 L 3 3 k 1 ( ) 3 2 M c = 4 4 L 3 3 k 1 ( ) 3 2 For these equations, the following relationships hold: L 2 = D Σ a

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Homework Set 3 Solutions - Homework 24 Solutions Due Friday...

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