The helium atomr1r2r2−r1−e−e2ezyx122221222rrerereVrrrr−+−−=Quantum numbers associated with electron spinSymbol Name Valuess spin angular momentum q. n. ½msspin magnetic q. n. ± ½j total angular momentum q. n. |ℓ ±s|Quantum numbers for atomsName related quantity valuesPrincipal quantum number n energy level n = 1, 2, 3, 4,…shell = K, L, M, N,…Angular momentum orbital angular l = 0, 1, 2, 3, ..., n-1quantum number l momentum orbital = s, p, d, f, …Magnetic quantum number mlz-component of ml= 0, ±1, ±2,…, ±lorbital angular momentumSpin quantum number msz-component of ms= ± ½spin angular momentumVector model of quantized angular momentum for ℓ = 11 ħ1 ħz-axismℓ= 1mℓ= 0mℓ= -1hll )1(|| +=LLz= mℓħh)1(|| += ssSsz= msħ|L| = 21/2ħTotal angular momentum vector JSLJrrr+=JLSh1)j(j|J| +=|s|j±=lExamples:when ℓ = 0, j = 1/2when ℓ = 1, j = 1/2, 3/2Atomic energy levels321Hydrogen-likeatomnn,ℓ3,23,13,02,02,11,0Multi-electron atom (without spin)Multi-electron atom (with spin)n,ℓ,j3,2,5/23,2,3/23,1,3/23,1,1/23,0,1/22,1,3/22,1,1/22,0,1/21,0,1/23,13,02,02,11,0Energy level diagram for a multi-electronn,ℓ,j2p½2s½2p3/21s½3s½3p3/22p½3d3/23d5/21s2s2p3s3p3d(without spin)(with spin)n,ℓThe Pauli exclusion principle:Each electron in a multi-electron atom must have a unique wavefunction.(No two electrons may have the same set of quantum numbers).1K0s0±1/2222L0s0±1/221p1,0,−1±1/2 6 83M102spd01,0,−12,1,0,−1,−2±1/2±1/2±1/22610 182n22(2ℓ+1)2ℓ+1Electron configurations and the aufbau principle1s 2s 3s 4s 5s 6s 7s2p 3p 4p 5p 6p 3d 4d 5d4f 5f1s2s2p3s3p3d4sElectron configurations of atoms2He10Ne18Ar36Kr54Xe1s21s22s22p6= [He]2s22p61s22s22p63s23p6= [Ne]3s23p61s22s22p63s23p63d104s24p6= [Ar] 3d104s24p61s22s22p63s23p63d104s24p64d105s25p6= [Kr] 4d105s25p6Outer-shell octet configurations are especially stable!Electron configurations of atoms (cont.)20Ca23V24Cr28Ni29Cu[Ar]4s2[Ar] 3d34s2[Ar] 3d54s1(Half filled subshells have extra stability)[Ar] 3d84s2[Ar] 3d104s1(Filled subshells have extra stability)Hund’s rule: If more than one orbital is available in a subshell,the lowest energy configuration is achieved by maximizing the number of unpaired electrons. 15P[Ne]3s23p3Example:3s3pOuter shell electron configurations and the long form of the periodic table representative elementstransition elementsInner transition elementsBinding Energies (eV)Kr Level Theory Expt.% Diff.1s 14328.06 14324.6 0.0242s 1925.49 1920.4 0.2642p1/21732.49 1729.7 0.1642p3/21680.06 1677.3 0.168XeLevelTheory Expt.% Diff.1s 34566.5 34565.1 0.0042s 5453.7 5452.9 0.0152p1/25108.1 5103.8 0.0842p3/24788.2 4782.2 0.127Atomic Number0 20406080100Ionization Potential (eV)0510152025HeLiNNeNaPArKZnKrRbCdXeCsLuHgRnTlPeriodic trends of ionization potentialsIP ~ E0(Z−σ)2/ n2Li(1.45)Na(1.80)K(2.20)Rb(2.35)Cs(2.60)Li(0.68)Na(0.98)K(1.33)Rb(1.48)Cs(1.67)F(0.50)Cl(1.00)Br(1.15)I(1.40)F(1.33)Cl(1.81)Br(1.96)I(2.19)+++++!!!!Periodic trends in atomic size (groups IA and 7A)r = a0n2/(Z−σ)Z−σ increases →n increases →Electronegativities of the elementsElectron affinityA−(g)→ A(g)+ e−electron affinity = ΔEExamples: Li = 60 kJ/molNa = 53 K = 48F = 328Cl = 149Br = 325C = 122N = −7O = 141Oxidation Number-4-3-2-1012345678HHeLiBeBCNOFNeNaMgAlSiPSClArKCaGaGeAsSeBrKrRbSrInSnSbTeIXeCsBaTlPbBiPoAtLanthanides andtransition metalsTransition metalsTransition metalsPeriodic trends of oxidation numbersN: 1s22s22p3Cl:
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