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# sol13 - 1 2 n r l = 5 5 5 E ¯ hω = 6 5 Degeneracy = 42...

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Introduction to Quantum Theory and Relativity PHYSICS 3740 Summer 2003 L. Burko Solutions for Homework Assignment #13 1. M = Am p = V ρ , V = Am p ρ , V A Am p = ρ ( 4 π 3 R 3 ) , R = ( 3 4 π Am p ) 1 / 3 , R A 1 / 3 Area = 4 πR 2 , R A 1 / 3 , Area A 2 / 3 2. 235 92 U 4 2 He + 231 90 Th Q = E (235 , 92) - E (4 , 2) - E (231 , 90) = - 12 MeV Should be positive for decay to take place. Instead result is negative and unreliable because of limited accuracy of given coefficients. Using measured masses from Appendix : M (235 , 92) - M (4 , 2) - M (231 , 90) = 0 . 005023 u = 4 . 679 MeV c 2 3. (a) 2 1 H + 29 14 Si 4 2 He + 27 13 Al (b) 2 1 H + 29 14 Si 1 1 H + 30 14 Si (c) 2 1 H + 29 14 Si 1 0 n + 30 15 P 4. E = ¯ (2 n r + l + 3 / 2) n r = 0 , 1 , 2 , ... , l = 0 , 1 , 2 , ... n r = 0 , l = 0 2 n r + l = 0 , E/ ¯ = 1 . 5 , Degeneracy = 2 , Magic = 2 n r = 0 , l = 1 2 n r + l = 1 , E/ ¯ = 2 . 5 , Degeneracy = 6 , Magic = 8 n r = 0 , 1 , l = 2 , 0 2 n r + l = 2 , 2 , E/ ¯ = 3 . 5 , Degeneracy = 12 , Magic = 20 n r = 0 , 1 , l = 3 , 1 2 n r + l = 3 , 3 , E/ ¯ = 4 . 5 , Degeneracy = 20 , Magic = 40 n r = 0 , 1 , 2 , l = 4 , 2 , 0 2 n r + l = 4 , 4 , 4 , E/ ¯ = 5 . 5 , Degeneracy = 30 , Magic = 70 n r = 0

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Unformatted text preview: 1 2 n r + l = 5 , 5 , 5 , E/ ¯ hω = 6 . 5 , Degeneracy = 42 , Magic = 112 n r = 0 , 1 , 2 , 3 , l = 6 , 4 , 2 , 2 n r + l = 6 , 6 , 6 , 6 , E/ ¯ hω = 7 . 5 , Degeneracy = 56 , Magic = 168 5. N 1 ( t ) = N 1 (0) e-R 12 t N 2 ( t ) = N 1 (0) R 12 e-R 23 t-e-R 12 t R 12-R 23 A 1 =-dN 1 dt = R 12 N 1 (0) e-R 12 t = 4 × 10 20 e-t 250 s-1 A 2 =-dN 2 dt = R 12 N 1 (0) R 23 e-R 23 t-R 12 e-R 12 t R 12-R 23 = 4 × 10 20 (0 . 739 e-t 588-1 . 740 e-t 250 ) s-1 1 6. τ = 200 ln 2 = 288 s R 1 R 2 = . 62 . 38 R = R 1 + R 2 = 1 τ = 1 288 R 2 = 1 . 32 × 10-3 s-1 R 1 = 2 . 15 × 10-3 s-1 2...
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