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It also contrasts earlier schematic approaches with Grotrian’s 1924 synthesis, emphasizing classification by orbital and spin quantum numbers.",{"@graph":14,"@context":71},[15,34,54],{"@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/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/from-the-history-of-physics-grotrian-diagrams/665331/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":48,"encodingFormat":47,"isAccessibleForFree":49,"interactionStatistic":50},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/from-the-history-of-physics-grotrian-diagrams/665331.png","ImageObject",300,407,{"name":42,"@type":43},"Blitz","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29",true,{"@type":51,"interactionType":52,"userInteractionCount":4},"InteractionCounter",{"@type":53},"ViewAction",{"@type":55,"mainEntity":56},"FAQPage",[57,63,67],{"name":58,"@type":59,"acceptedAnswer":60},"Why did Grotrian diagrams become important in physics practice?","Question",{"text":61,"@type":62},"They became a habitual and indispensable element of professional language because they make complex spectral-term and transition information easier to visualize and reason about.","Answer",{"name":64,"@type":59,"acceptedAnswer":65},"How are spectral terms linked to atomic energy states in the text?",{"text":66,"@type":62},"Bohr related the spectral term to the energy of an atomic stationary state, so the relationship supports conservation of energy for radiation transitions between stationary states.",{"name":68,"@type":59,"acceptedAnswer":69},"What changed with Bohr’s and later Grotrian’s graphical methods?",{"text":70,"@type":62},"Bohr introduced a graphic representation of stationary atomic states, using energy as the main independent variable. Grotrian’s 1924 step combined earlier ideas and redesigned the axes: energy pointed upwards while classification of states used orbital and spin quantum numbers.","https://schema.org",{"og:url":32,"og:type":73,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":75,"canonical":32},"index,follow",{"doc_id":77,"site_id":7},665331,1793298343,{"code":4,"msg":80,"data":81},"success",[82,86,90,94,99,104,109,113,118,121,125],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":83,"show_sort_weight":84,"slug":85},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":87,"show_sort_weight":88,"slug":89},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},"Exam",70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":111,"slug":112},8,30,"research-report",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},9,"Religion & Spirituality",20,"religion-spirituality",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":116,"slug":120},"World Cup","world-cup",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":122,"slug":124},10,"Lifestyle","lifestyle",{"id":126,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":95,"slug":128},19,"General","general",{"code":4,"msg":80,"data":130},{"doc_id":77,"user_id":131,"nickname":42,"user_avatar":132,"doc_module":4,"category_id":110,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":4,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":138,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":12,"update_tm":78,"read_time":122},24464137899374,"https://us-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","FROM THE HISTORY OF PHYSICS PACS numbers: 01.65.+g, 32.30.±r  \nGrotrian diagrams  \nS G Rautian, A S Yatsenko  \n70 years have passed since the publication of a widely renowned book Graphische Darstellung der Spektren von Atomen und Ionen mit Ein, Zwei und Drei Valentzelektronen (Graphic Representation of Spectra of Atoms and Ions with One, Two and Three Valence Electrons) by W Grotrian [1], which has played an enviable role in atomic spectroscopy and the quantum mechanics of atomic systems. Grotrian diagrams have long become an habitual and indispensable element of the professional language of physicists and chemists and it is now difficult to perceive how we could obviate the need for them. Meanwhile nearly 15 years had elapsed since the enunciation of the quantum postulates by N Bohr in 1913 [2] and the issue of the `hero of our narration'. The explanation for such a long period of time is certainly associated with a radical transformation of basic ideas in physics.  \nBy 1913, the spectroscopists had amassed extensive factual data for the frequencies of emission and absorption spectral lines. Summing up `` ... a 60-year scientific activity resulting in fifteen thousand works'' Professor D S Rozhdestvenski wrote in 1915: ``All the elements acquired their own characteristics in the lists of spectral lines..., these lists are nearly concluded, the wavelengths are occasionally measured to an astonishing precision..., empirical relationships between wavelengths of spectral lines have been established'' [3] .  \nThe wavenumbers of lines are governed by Rydberg's formula to an `astonishing accuracy' as well:  \nn21 􀂈 T2 􀂅n2 􀂆ÿ T1 􀂅n1 􀂆 ; T􀂅n􀂆 􀂈 􀂅n~~ ~~􀂇~~ ~~a~~ ~~R􀂇~~ ~~b=n2~~ ~~􀂆~~ ~~2 ; 􀂅1􀂆  \nwhere n is an integer, and R, a and b are constants. The quantity T􀂅n􀂆 had been referred to as `the spectral term', and later, when the etymology of the word was forgotten, simply as `the term' (using the English word) . N Bohr related the term to the energy of an atomic stationary state and relationship (1) was assigned the meaning of the law of conservation of energy for the atomic radiation transition from one stationary state to another.  \nSince spectral lines can be calculated with the use of terms, the latter are of much more importance in studies of atomic spectra than the former. The variety of lines is much wider  \nS G Rautian, A S Yatsenko Institute of Automatics and Electrometry, Siberian Branch of the Russian Academy of Sciences  \n630090 Novosibirsk, Akad. V A Koptyug prospekt 1  \nTel. (7-3832) 33 37 75, 39 92 56; Fax (7-3832) 33 38 63  \nE-mail: [fractal@iae.nsk.su](fractal@iae.nsk.su), [uv-laser@iaie-phys.nsk.su](uv-laser@iaie-phys.nsk.su)  \nReceived 24 March 1998  \nUspekhi Fizicheskikh Nauk 169 (2) 217 ± 220 (1999)  \nTranslated by A Radzig; edited by M S Aksent'eva  \nthan a relatively simple collection of terms, which in fact reflect individual peculiarities of a particular atom. It is extremely complicated, however, to obtain a spectral series (1) on a basis of tables of wavelengths. Professor G S Landsberg wrote in this connection in his review article [4]:``Not without reason Paschen says that your attempts at searching for a series from the examination of tables of spectral lines are hopeless `if you are not Rydberg''. In this situation, the graphical methods of analysis played an important part.  \nIt is a matter of general experience that graphs illustrating a great diversity of functions, for example, the dependence of potential energy on distance, U􀂅x􀂆, hold much favour in classical physics. The peculiarities of a graph instantaneously strike our eyes and it is frequently more useful for forming a qualitative picture of the physical processes involved than analysis of the explicit formula describing the behaviour of U􀂅x􀂆 . The terms `potential well', `potential barrier', `turning point', etc., being obviously thrusted by the geometrical associations (the word composition of the language always reflects the point of the matt","cbCaivBDYBic7grK","https://ap.wps.com/l/cbCaivBDYBic7grK","pdf",153451,"English","# Historical background\n## Spectral lines, terms, and the Rydberg relation\n## Graphical representations in atomic spectroscopy\n## From Bohr and Rozhdestvenski to Grotrian diagrams","[{\"question\":\"Why did Grotrian diagrams become important in physics practice?\",\"answer\":\"They became a habitual and indispensable element of professional language because they make complex spectral-term and transition information easier to visualize and reason about.\"},{\"question\":\"How are spectral terms linked to atomic energy states in the text?\",\"answer\":\"Bohr related the spectral term to the energy of an atomic stationary state, so the relationship supports conservation of energy for radiation transitions between stationary states.\"},{\"question\":\"What changed with Bohr’s and later Grotrian’s graphical methods?\",\"answer\":\"Bohr introduced a graphic representation of stationary atomic states, using energy as the main independent variable. Grotrian’s 1924 step combined earlier ideas and redesigned the axes: energy pointed upwards while classification of states used orbital and spin quantum numbers.\"}]","FROM THE HISTORY OF PHYSICS - Grotrian Diagrams | PDF"]