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It introduces the principal (n), angular (l), and magnetic (m) quantum numbers and connects them to orbital size, shape, and spatial orientation. The text then lays out rules for allowed integer values and combinations, followed by how shells and subshells form using two-character notations such as 2p and 4f. It summarizes orbital counts and orientations for n=1 to n=3.",{"@graph":63,"@context":123},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/quantum-numbers-and-electron-configurations-quantum-numbers-and-allowed-combinations-shells-and-subshells/566557/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/quantum-numbers-and-electron-configurations-quantum-numbers-and-allowed-combinations-shells-and-subshells/566557.png","ImageObject",442,249,{"name":88,"@type":89},"BigDaveOnline","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-27","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",8,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115,119],{"name":106,"@type":107,"acceptedAnswer":108},"How do the principal (n), angular (l), and magnetic (m) quantum numbers relate to orbital properties?","Question",{"text":109,"@type":110},"The principal quantum number n determines orbital size. The angular quantum number l describes the orbital shape, and the magnetic quantum number m specifies the orbital’s orientation in space.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What are the allowed-value rules for n, l, and m?",{"text":114,"@type":110},"The quantum numbers n, l, and m are integers, with n not equal to zero. The value of l can range from 0 to n−1, and m can range from −l to +l.",{"name":116,"@type":107,"acceptedAnswer":117},"How do shells and subshells organize orbitals, and what do codes like 2p and 4f mean?",{"text":118,"@type":110},"Orbitals with the same n form a shell, and orbitals within a shell sharing the same l form subshells. Codes use the first character for the shell (n) and the second letter for the subshell type, with s(l=0), p(l=1), d(l=2), and f(l=3).",{"name":120,"@type":107,"acceptedAnswer":121},"How many orbitals are in shells and subshells, and what pattern governs them?",{"text":122,"@type":110},"The number of orbitals in a shell equals n² (so 1, 4, and 9 for n=1,2,3). In a subshell, the number of orbitals equals 2l+1, giving 1 for s, 3 for p, and 5 for d subshells.","https://schema.org",{"og:url":78,"og:type":125,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":127,"canonical":78},"index,follow",{"doc_id":129,"site_id":56},566557,1792013028,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":88,"user_avatar":134,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":140,"language":141,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":61,"update_tm":145,"read_time":76},962090896214,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Quantum Numbers and Electron Configurations  \nQuantum Numbers  \nThe Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. Schrodinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found.  \nThe three coordinates that come from Schrodinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.  \nThe principal quantum number (n) describes the size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2) . The principal quantum number therefore indirectly describes the energy of an orbital.  \nThe angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2) . They can even take on more complex shapes as the value of the angular quantum number becomes larger.  \nThere is only one way in which a sphere (l = 0) can be oriented in space. Orbitals that have polar (l = 1) or cloverleaf (l = 2) shapes, however, can point in different directions. We therefore need a third quantum number, known as the magnetic quantum number (m), to describe the orientation in space of a particular orbital. (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)  \nRules Governing the Allowed Combinations of Quantum Numbers  \n· The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on.  \n· The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on.  \n· The angular quantum number (l) can be any integer between 0 and n-1. If n = 3, for example, l can be either 0, 1, or 2.  \n· The magnetic quantum number (m) can be any integer between-l and +l. If l = 2, m can be either-2, -1, 0, + 1, or +2.  \nShells and Subshells of Orbitals  \nOrbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number. Chemists describe the shell and subshell in which an orbital belongs with a two-character code such as 2p or  \n4f. The first character indicates the shell (n = 2 or n = 4) . The second character identifies the subshell. By convention, the following lowercase letters are used to indicate different subshells.  \ns: l = 0  \np: l = 1  \nd: l = 2  \nf: l = 3  \nAlthough there is no pattern in the first four letters (s, p, d, f), the letters progress alphabetically from that point (g, h, and so on) . Some of the allowed combinations of the n and l quantum numbers are shown in the figure below.  \nThe third rule limiting allowed combinations of the n, l, and m quantum numbers has an important consequence. It forces the number of subshells in a shell to be equal to the principal quantum number for the shell. The n = 3 shell, for example, contains three subshells: the 3s, 3p, and 3d orbitals.  \nPossible Combinations of Quantum Numbers  \nThere is only one orbital in the n = 1 shell because there is only one way in which a sphere can be oriented in space. The only allowed combination of quantum numbers for which n = 1 is the following.  \nn l m  \n1 0 0 1s  \nThere are four orbitals in the n = 2 shell.  \nn l m  \n2 0 0 2s","cbCaiug2eGAymAkC","https://ap.wps.com/l/cbCaiug2eGAymAkC","pdf",94771,9,"English","# Quantum Numbers\n## Bohr vs. Schrödinger model\n## Principal (n), angular (l), magnetic (m) quantum numbers\n# Rules Governing Allowed Combinations of Quantum Numbers\n# Shells and Subshells of Orbitals\n## Two-character shell/subshell codes\n## Orbital counts in shells and subshells\n# Possible Combinations for n=1 to n=3\n## 1s, 2s/2p, and 3s/3p/3d orbitals\n## Orientation of d orbitals","[{\"question\":\"How do the principal (n), angular (l), and magnetic (m) quantum numbers relate to orbital properties?\",\"answer\":\"The principal quantum number n determines orbital size. The angular quantum number l describes the orbital shape, and the magnetic quantum number m specifies the orbital’s orientation in space.\"},{\"question\":\"What are the allowed-value rules for n, l, and m?\",\"answer\":\"The quantum numbers n, l, and m are integers, with n not equal to zero. The value of l can range from 0 to n−1, and m can range from −l to +l.\"},{\"question\":\"How do shells and subshells organize orbitals, and what do codes like 2p and 4f mean?\",\"answer\":\"Orbitals with the same n form a shell, and orbitals within a shell sharing the same l form subshells. Codes use the first character for the shell (n) and the second letter for the subshell type, with s(l=0), p(l=1), d(l=2), and f(l=3).\"},{\"question\":\"How many orbitals are in shells and subshells, and what pattern governs them?\",\"answer\":\"The number of orbitals in a shell equals n² (so 1, 4, and 9 for n=1,2,3). In a subshell, the number of orbitals equals 2l+1, giving 1 for s, 3 for p, and 5 for d subshells.\"}]","Quantum Numbers and Electron Configurations - Quantum Numbers and Allowed Combinations - Shells and Subshells | PDF",1791862805]