[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-566553-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-566553-en":127},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","quantum-numbers-atomic-orbitals-and-electron-configurations-atomic-orbitals-and-electron-configurations","QUANTUM NUMBERS, ATOMIC ORBITALS, AND ELECTRON CONFIGURATIONS - Atomic Orbitals and Electron Configurations","","Wave functions from solving the Schrödinger equation define the probability of finding electrons at specific energy levels, leading to the concept of atomic orbitals as regions of high electron probability. Each electron is described by four quantum numbers: principal (n) for energy and shell size, angular momentum (l) for orbital shape and subshells, magnetic (ml) for spatial orientation, and spin (ms) for spin direction. The Pauli exclusion principle limits occupancy and determines paired versus unpaired electrons, relating to diamagnetic and paramagnetic behavior. Electron configurations are filled by the Aufbau principle and can be written using orbital notation or orbital diagrams, distinguishing ground and excited states.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/general/","General",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/quantum-numbers-atomic-orbitals-and-electron-configurations-atomic-orbitals-and-electron-configurations/566553/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/quantum-numbers-atomic-orbitals-and-electron-configurations-atomic-orbitals-and-electron-configurations/566553.png","ImageObject",442,249,{"name":42,"@type":43},"lilac","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What do quantum numbers represent for electrons in an atom?","Question",{"text":63,"@type":64},"Electrons in an atom are described by four quantum numbers: n identifies the energy level and shell, l determines orbital shape and subshell, ml gives the orbital’s spatial orientation, and ms specifies the spin direction.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does the Pauli exclusion principle affect electrons in the same orbital?",{"text":68,"@type":64},"No two electrons in the same atom can have identical values for all four quantum numbers. Therefore, at most two electrons can occupy the same orbital, and they must have opposite spins.",{"name":70,"@type":61,"acceptedAnswer":71},"How are electron configurations constructed using the Aufbau principle?",{"text":72,"@type":64},"Electrons fill orbitals in an order corresponding mostly to increasing subshell energy (such as 1s, 2s, 2p, 3s...). Configurations are written by indicating the occupied orbitals and using superscripts to show how many electrons occupy each set.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},566553,1792107655,{"code":4,"msg":82,"data":83},"success",[84,89,94,99,104,109,114,119,124],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":86,"show_sort_weight":87,"slug":88},11,"Presentations",90,"presentations",{"id":90,"doc_module":22,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},12,"Resumes",80,"resumes",{"id":95,"doc_module":22,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},14,"Invoices",70,"invoices",{"id":100,"doc_module":22,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},15,"Posters",60,"posters",{"id":105,"doc_module":22,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},16,"Social Media",50,"social-media",{"id":110,"doc_module":22,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},17,"Forms",40,"forms",{"id":115,"doc_module":22,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},18,"Letters",30,"letters",{"id":120,"doc_module":22,"doc_module_name":25,"category_name":121,"show_sort_weight":122,"slug":123},21,"Paper Templates",5,"papers-templates",{"id":125,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":4,"slug":126},158,"general-158",{"code":4,"msg":82,"data":128},{"doc_id":79,"user_id":129,"nickname":42,"user_avatar":130,"doc_module":22,"category_id":125,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":136,"language":137,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":12,"update_tm":141,"read_time":30},3985747861865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","QUANTUM NUMBERS, ATOMIC ORBITALS, AND ELECTRON CONFIGURATIONS  \nQuantum Numbers and Atomic Orbitals  \nBy solving the Schrödinger equation (Hψ = E ψ ), we obtain a set of mathematical equations, called wave functions (ψ ), which describe the probability of finding electrons at certain energy levels within an atom.  \nA wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon oflight) .  \nEach electron in an atom is described by four different quantum numbers. The first three (n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital.  \n1. Principal Quantum Number (n): n = 1, 2, 3,…, 8.  \nSpecifies the energy of an electron and the size of the orbital (the distance from the nucleus of the peak in a radial probability distribution plot) . All orbitals that have the same value of n are said to be in the same shell (level) . For a hydrogen atom with n=1, the electron is in its ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of orbitals for a given n value is n2.  \n2. Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1.  \nSpecifies the shape of an orbital with a particular principal quantum number. The secondary quantum number divides the shells into smaller groups of orbitals called subshells (sublevels ) . Usually, a letter code is used to identify l to avoid confusion with n:  \nl 0 1 2 3 4 5    \nLetter s p d f g h . . .  \nThe subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and soon. The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s \u003C p \u003C d \u003C f) .  \n3. Magnetic Quantum Number (ml): ml = -l, ..., 0, ..., +l.  \nSpecifies the orientation in space of an orbital of a given energy (n) and shape (l) . This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. Thus the s subshell has only one orbital, the p subshell has three orbitals, and so on.  \n4. Spin Quantum Number (ms): ms = +½ or-½.  \nSpecifies the orientation of the spin axis of an electron. An electron can spin in only one of two directions (sometimes called up and down) .  \nThe Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same atom can have identical values for all four of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins.  \nBecause an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other; the spins are said to be paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in one direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.  \nTable of Allowed Quantum Numbers  \nNumber of Orbital Number of  \n n   l   ml   orbitals   Name electrons  \n1 0 0 1 1s 2  \n2 0 0 1 2s 2  \n1 -1, 0, +1 3 2p 6  \n3  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n4  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n5  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \n____ ____________ ____ ____ ____  \nWriti","cbCaivSZ0TEKIGLd","https://ap.wps.com/l/cbCaivSZ0TEKIGLd","pdf",508026,9,"English","# Quantum Numbers and Atomic Orbitals\n## Principal Quantum Number (n)\n## Angular Momentum Quantum Number (l)\n## Magnetic Quantum Number (ml)\n## Spin Quantum Number (ms)\n# Writing Electron Configurations\n## Aufbau principle\n## Orbital diagrams and Hund’s rule\n## Ground state vs excited state\n# Properties of Monatomic Ions","[{\"question\":\"What do quantum numbers represent for electrons in an atom?\",\"answer\":\"Electrons in an atom are described by four quantum numbers: n identifies the energy level and shell, l determines orbital shape and subshell, ml gives the orbital’s spatial orientation, and ms specifies the spin direction.\"},{\"question\":\"How does the Pauli exclusion principle affect electrons in the same orbital?\",\"answer\":\"No two electrons in the same atom can have identical values for all four quantum numbers. Therefore, at most two electrons can occupy the same orbital, and they must have opposite spins.\"},{\"question\":\"How are electron configurations constructed using the Aufbau principle?\",\"answer\":\"Electrons fill orbitals in an order corresponding mostly to increasing subshell energy (such as 1s, 2s, 2p, 3s...). Configurations are written by indicating the occupied orbitals and using superscripts to show how many electrons occupy each set.\"}]","QUANTUM NUMBERS, ATOMIC ORBITALS, AND ELECTRON CONFIGURATIONS - Atomic Orbitals and Electron Configurations | PDF",1791862799]