lecture_9_07b - Angular momentum is quantized mvr where n 1,2 2 2 2 Bohr's quantum condition h n 2 2 n n n 2 2 2 squaring m v 2 so mv 2 r mr n 2 2 Ze 2

lecture_9_07b - Angular momentum is quantized mvr where n...

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05/13/09 Physics 13 - Fall 2001 - Goldstein 1 Bohr’s quantum condition Angular momentum is quantized mvr = n h 2 p = n h where n = 1,2,... squaring m 2 v 2 = n 2 h 2 r 2 , so mv 2 = n 2 h 2 mr 2 . Substituting for mv 2 yields n 2 h 2 mr 2 = k EM Ze 2 r Then allowed orbits have r n = n 2 h 2 k EM Ze 2 m = n 2 Z a 0
05/13/09 Physics 13 - Fall 2001 - Goldstein 2 Quantized orbits Bohr radius a 0 = h 2 k EM e 2 m = 5.29 10 - 11 m = 0.529 A Substitute for r in E: E n = - 1 2 k EM Z e 2 r n = k EM 2 e 4 mZ 2 2h 2 n 2 or E n = - Z 2 n 2 E 0 with E 0 = 13.6 eV So - E 0 is the lowest Energy "state"
05/13/09 Physics 13 - Fall 2001 - Goldstein 3 Radiative transitions Quantum jump occurs electron jumps from orbit i to f which releases photon h ν = Ε ι - Ε φ νοτε τηαττηισισΓρεεκ λεττερ νυ τηεν ν = Ζ 2 Ε 0 2 π η 1 ν φ 2 - 1 ν ι 2 Ρψδβεργ φορμ υλα! ανδ Ρ = Ε 0 / η ϖηιχηισιν εξαχταγρεεμ εντ
05/13/09 Physics 13 - Fall 2001 - Goldstein 4 Transition example from zebu.uoregon.edu/~js/glossary/bohr_atom.html
05/13/09 Physics 13 - Fall 2001 - Goldstein 5 Energy levels of H E 0 eV -0.85 eV -1.5 eV -3.4 eV -13.6 eV 1 2 3 4 n ground state continuum
05/13/09 Physics 13 - Fall 2001 - Goldstein 6 Spectral lines of H Transitions: n = 6 2;5 2;4 2; 3 2
05/13/09 Physics 13 - Fall 2001 - Goldstein 7 deBroglie waves Why does the quantization condition work?