Spectroscopy Cheat Sheet, Study notes of Chemistry

Download Spectroscopy Cheat Sheet and more Study notes Chemistry in PDF only on Docsity! Spectroscopy Cheat Sheet Atomic Spectroscopy • Energy of hydrogen atom En = ( Z2ħ2 2µa2 µ ) 1 n2 (1) aµ = 4πε0ħ2 µe2 = me µ a0 (2) • Mean radii of hydrogen atom〈 1 r 〉 ∝ Z n2 (3) 〈r〉 = aµn2(1+ (1− l(l+1)/n2)/2) (4) • Spin-orbit coupling arises due to electron spin magnetic moment in- teracting with magnetic moment generated by nuclear charge orbiting electron in electron rest frame. This effect is proportional to the mag- netic interaction ∝ 〈 1/r3〉 and the nuclear charge Z, so overall you would expect SO coupling to be proportional to Z4. In fact〈 1 r3 〉 = 2 a3 µn3l(l+1)(2l+1) (5) • Selection rules. For optically allowed transitions ∆n = anything (6) ∆l =±1 from conservation of angular momentum and parity (7) ∆ml = 0,±1 from conservation of angular momentum (8) ∆s = 0 from conservation of spin (9) ∆ms = 0 (10) ∆ j = 0,±1 (no j = 0→ 0) conservation of angular momentum (11) ∆m j = 0,±1 (12) These are the same for many electron atoms with l,ml , j,m j, s,ms re- placed by L, ML, J, MJ ,S, MS. • Zeeman effect splits levels with angular momentum EZeeman =µB gJBMJ (13) gJ = 1+ J(J+1)−L(L+1)+S(S+1) 2J(J+1) (14) 1