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Solutions Atomic Physics for FYSC11 16-03-21. 1. Z = 5 i.e. B+4 2a. Yes Lˆz . Eigenvalue . 2 2b. No Lˆ2 5 2c. Lˆz 2d. 26 Lˆ2 5 2 (Y1,1 6Y2,1 ) 2 3a. 5s is more tightly bound since an s-electron penetrates the core more that a d-electron, larger quantum defect. 3b. Tnd Eion End End RM ζ 2 RM ζ 2 δ n . ζ 1. RM R (n δ )2 Tnd 1 1 in cm 1. λ(3s 3 p ) λ(3 p nd ) From this we approximate δ(8d) = 0.015 giving T (8d ) 1721 cm1 E (8d ) 39728 cm1 λ(3 p 8d ) 4393.5 Å. Experimental value is 4393.4 Å. 4a. The Doppler width is given by: 7 f D 7.16 10 (g/mol) K 4b. 2 0 2nt cos 1/2 1/2 3 108 m/s 2000 K 0.296 GHz 6 2.776 10 m 137 g/mol 4 t f with n = 1 and θ = 0. c dδ 4πt c c 1 R 3 108 m/s 0.1 Δf Δδ 1.68 GHz. df c 4πt 2πt R 2π 3 103 m 0.9 The experiment would be limited by the resolution of the Fabry-Perot interferometer Thus 5ab. Parallel to the field we only observe the (circularly polarized) σ± components arising when ΔMJ = ±1 5c. Emin 3 /4 B B 9.27 1024 J 57.6 μeV = 13.93 GHz. Yes we can resolve the Zeeman structure with our Fabry-Perot. 6a. 6b. 6c. ΔE(5/2-3/2) = 1860 + 892 = 2752 MHz. Using the Landé interval rule this gives A = 2752/2.5 = 1101 MHz. ΔE(3/2-1/2) = 2600 - 892 = 1708 MHz. Using the Landé interval rule this gives A = 1708/1.5 = 1139 MHz. Best estimate is the average A = 1120 MHz.