[{"data":1,"prerenderedAt":134},["ShallowReactive",2],{"cheatsheet-electron-structure-and-light":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"electron-structure-and-light",[5],12,"Electron Structure & Light","Quantum numbers, orbital filling, electron configurations, and the light/energy relationships.",[11,23,51,59,67,75,83,92,105,113,126],{"heading":12,"kind":13,"items":14},"Quantum numbers","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","EL-R001","transform","original","n = 1, 2, 3, … . For each n, ℓ = 0 to n−1. For each ℓ, mₗ = −ℓ to +ℓ in integer steps. mₛ = +½ or −½.","8d21f6136797bd6b9643248b3cd5fda80cf2590a5d99647f769b920b89ec448b",{"heading":24,"kind":25,"columns":26,"items":30},"Subshell codes","data",[27,28,29],"ℓ","Letter","Max e⁻",[31],{"ref":32,"mode":19,"provenance":20,"rows":34,"source_hash":50},{"type":17,"topic":7,"id":33,"field":17},"EL-R002",[35,39,43,46],[36,37,38],"0","s","2",[40,41,42],"1","p","6",[38,44,45],"d","10",[47,48,49],"3","f","14","d1825bf7954c346d181a8d38df53e0cab1a1716579a3571944a5ee2b44f55254",{"heading":52,"kind":13,"items":53},"Electrons per subshell",[54],{"ref":55,"mode":19,"provenance":20,"text":57,"source_hash":58},{"type":17,"topic":7,"id":56,"field":17},"EL-R003","A subshell holds 2(2ℓ+1) electrons: s = 2, p = 6, d = 10, f = 14.","d066f92020070ed2132b2d015d0c0af1bf8082bfb2e445bca7274fe8d6e73f6b",{"heading":60,"kind":13,"items":61},"Pauli exclusion",[62],{"ref":63,"mode":19,"provenance":20,"text":65,"source_hash":66},{"type":17,"topic":7,"id":64,"field":17},"EL-R004","No two electrons in an atom share all four quantum numbers. One orbital (n, ℓ, mₗ) holds at most 2 electrons, with opposite spins.","b6f5e6d2ba5e94b01acaf3e0f66b74eab9c1d3352c7c50c4a40b8baa25398e50",{"heading":68,"kind":13,"items":69},"Aufbau fill order",[70],{"ref":71,"mode":19,"provenance":20,"text":73,"source_hash":74},{"type":17,"topic":7,"id":72,"field":17},"EL-R005","Fill by increasing energy: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p.","b72c0226d90acaa91af9b8c3eda46498f3112e94341ab290e1e89d57b6e7f2d5",{"heading":76,"kind":13,"items":77},"Hund's rule",[78],{"ref":79,"mode":19,"provenance":20,"text":81,"source_hash":82},{"type":17,"topic":7,"id":80,"field":17},"EL-R006","Within a degenerate subshell, place one electron in each orbital (parallel spins) before pairing. Maximum-multiplicity ground state is most stable.","9b242cafd6f4402576eddd492ccf1a120645e552284072e9af207c536720d17a",{"heading":84,"kind":85,"items":86},"Cr & Cu exceptions","pitfalls",[87],{"ref":88,"mode":19,"provenance":20,"text":90,"source_hash":91},{"type":17,"topic":7,"id":89,"field":17},"EL-R009","Cr = [Ar] 4s¹ 3d⁵ and Cu = [Ar] 4s¹ 3d¹⁰ (also Mo, Ag, Au): half-filled d⁵ and filled d¹⁰ stability beats the naive Aufbau prediction.","9b84953453a6d25da9339e377c80892541c30c0d1d404fa1e3972a857d428c55",{"heading":93,"kind":13,"items":94},"Ion configurations",[95,100],{"ref":96,"mode":19,"provenance":20,"text":98,"source_hash":99},{"type":17,"topic":7,"id":97,"field":17},"EL-R007","Cations lose the highest-n (ns) electrons first, before (n−1)d: Fe [Ar] 4s² 3d⁶ → Fe³⁺ [Ar] 3d⁵.","7ee5e26907e1afe08ca9ff6a9c8732b74b0af415fbe2a4fc3b904bd2663bbdfb",{"ref":101,"mode":19,"provenance":20,"text":103,"source_hash":104},{"type":17,"topic":7,"id":102,"field":17},"EL-R008","Anions add electrons in Aufbau order to the next noble gas: O [He] 2s² 2p⁴ + 2e⁻ → O²⁻ [Ne].","65def9152789b9345e43bd52d15cbd43d9fb64698d4958dd94a5ffc91f931b0b",{"heading":106,"kind":13,"items":107},"Photon energy",[108],{"ref":109,"mode":19,"provenance":20,"text":111,"source_hash":112},{"type":17,"topic":7,"id":110,"field":17},"EL-R010","E = hν and c = λν, so E = hc/λ. h = 6.626 × 10⁻³⁴ J·s, c = 2.998 × 10⁸ m/s. Higher frequency = shorter wavelength = higher energy.","5d739c8b83471d0a24468b7147ef93349ffc3a3a39b9daa7e396fcb4bbc6a275",{"heading":114,"kind":13,"items":115},"Bohr energies & transitions",[116,121],{"ref":117,"mode":19,"provenance":20,"text":119,"source_hash":120},{"type":17,"topic":7,"id":118,"field":17},"EL-R011","Hydrogen-like orbital energy: Eₙ = −2.179 × 10⁻¹⁸ J · Z² / n² (Z = 1 for H).","7c2444fb317cef5bea66a8328f550db785f7133bbb6f35b7aa245d4bc2137792",{"ref":122,"mode":19,"provenance":20,"text":124,"source_hash":125},{"type":17,"topic":7,"id":123,"field":17},"EL-R012","Transition: ΔE = E_f − E_i (emit if \u003C 0, absorb if > 0). Photon wavelength λ = hc / |ΔE|.","02d8d13ab41cd253fa9c4061e8cb188a39e7988400c0eae29e4767c029b30c4f",{"heading":127,"kind":13,"items":128},"de Broglie wavelength",[129],{"ref":130,"mode":19,"provenance":20,"text":132,"source_hash":133},{"type":17,"topic":7,"id":131,"field":17},"EL-R013","λ = h / (m·v) = h/p, for a particle of mass m and velocity v. Use SI units (kg, m/s, J·s); λ comes out in metres. Larger momentum (m·v) gives a shorter wavelength.","f4a0806716bbcacb3e85e28c71d4e5a93119bc207fd35671954c29860bc302b3",1787246033461]