[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-327023-105":59,"doc-detail-327023-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","the-quantum-mechanics-of-atoms-and-molecules-introduction","The quantum mechanics of atoms and molecules - Introduction","","Introduction traces how nineteenth-century limits on learning stellar properties were overcome by spectroscopy, leading from Kirchoff’s sun discoveries to the spectroscope’s role in identifying elements and inferring compositions. It recounts the empirical progress from Balmer and Ritz formulas for hydrogen line spectra to the need for deeper atomic theory. The narrative then links Planck’s blackbody quantization and Einstein’s photoelectric explanation (photons) to the emergence of quantum ideas, while earlier electron evidence and Rutherford’s nuclear model set the stage for understanding atomic structure.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/the-quantum-mechanics-of-atoms-and-molecules-introduction/327023/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/the-quantum-mechanics-of-atoms-and-molecules-introduction/327023.png","ImageObject",300,407,{"name":92,"@type":93},"Sage","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How did spectroscopy change what could be learned about stars?","Question",{"text":112,"@type":113},"Spectroscopy enabled determination of intensive stellar properties such as temperature and composition by analyzing spectral lines. Techniques like prism dispersion and later spectroscopes made these insights possible.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What did the Balmer and Ritz formulas accomplish?",{"text":117,"@type":113},"They provided empirical ways to fit hydrogen’s emission wavelengths across spectral regions. Ritz’s modification unified line spectra using a single constant, guiding later theory development.",{"name":119,"@type":110,"acceptedAnswer":120},"Why did Planck’s and Einstein’s work matter for the development of quantum theory?",{"text":121,"@type":113},"Planck derived the blackbody radiation spectrum by assuming energy is quantized as multiples of hν. Einstein used the same quantum idea to explain the photoelectric effect, showing that light energy is absorbed in quanta (photons).","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},327023,1790487420,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},687197207057,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","-1-  \nA1.1 The quantum mechanics of atoms and molecules  \nJohn F Stanton  \nA1 .1.1 INTRODUCTION  \nAt the turn of the 19th century, it was generally believed that the great distance between earth and the stars would forever limit what could be learned about the universe. Apart from their approximate size and distance from earth, there seemed to be no hope of determining intensive properties of stars, such as temperature and composition. While this pessimistic attitude may seem quaint from a modern perspective, it should be remembered that all knowledge gained in these areas has been obtained by exploiting a scientific technique that did not exist 200 years ago—spectroscopy.  \nIn 1859, Kirchoff made a breakthrough discovery about the nearest star—our sun. It had been known for sometime that a number of narrow dark lines are found when sunlight is bent through a prism. These absences had been studied systematically by Fraunhofer, who also noted that dark lines can be found in the spectrum of other stars; furthermore, many of these absences are found at the same wavelengths as those in the solar spectrum. By burning substances in the laboratory, Kirchoff was able to show that some of the features are due to the presence of sodium atoms in the solar atmosphere. For the first time, it had been demonstrated that an element found on our planet is not unique, but exists elsewhere in the universe. Perhaps most important, the field of modern spectroscopy was born.  \nArmed with the empirical knowledge that each element in the periodic table has a characteristic spectrum, and that heating materials to a sufficiently high temperature disrupts all interatomic interactions, Bunsen and Kirchoff invented the spectroscope, an instrument that atomizes substances in a flame and then records their emission spectrum. Using this instrument, the elemental composition of several compounds and minerals were deduced by measuring the wavelength of radiation that they emit. In addition, this new science led to the discovery of elements, notably caesium and rubidium.  \nDespite the enormous benefits of the fledgling field of spectroscopy for chemistry, the underlying physical processes were completely unknown a century ago. It was believed that the characteristic frequencies of elements were caused by (nebulously defined) vibrations of the atoms, but even a remotely satisfactory quantitative theory proved to be elusive. In 1885, the Swiss mathematician Balmer noted that wavelengths in the visible region of the hydrogen atom emission spectrum could be fitted by the empirical equation  \n(A1.1.1)  \nwhere m = 2 and n is an integer. Subsequent study showed that frequencies in other regions of the hydrogen spectrum could be fitted to this equation by assigning different integer values to m, albeit with a different value of the constant b. Ritz noted that a simple modification of Balmer’s formula  \n(A1.1.2)  \n-2-  \nsucceeds in fitting all the line spectra corresponding to different values of m with only the single constant RH. Although this formula provides an important clue regarding the underlying processes involved in spectroscopy, more than two decades passed before a theory of atomic structure succeeded in deriving this equation from first principles.  \nThe origins of line spectra as well as other unexplained phenomena such as radioactivity and the intensity profile in the emission spectrum of hot objects eventually led to a realization that the physics of the day was incomplete. New ideas were clearly needed before a detailed understanding of the submicroscopic world of atoms and molecules could be gained. At the turn of the 20th century, Planck succeeded in deriving an equation that gave a correct description of the radiation emitted by an idealized isolated solid (blackbody radiation). In the derivation, Planck assumed that the energy of electromagnetic radiation emitted by the vibrating atoms of the solid cannot have just any energy, but must be an integra","cbCaisIBqKyEYzGK","https://ap.wps.com/l/cbCaisIBqKyEYzGK","pdf",71670857,3076,"English","# Introduction\n## Spectroscopy and stellar composition\n## Line spectra and empirical formulas\n## Planck and blackbody radiation\n## Einstein and the photoelectric effect","[{\"question\":\"How did spectroscopy change what could be learned about stars?\",\"answer\":\"Spectroscopy enabled determination of intensive stellar properties such as temperature and composition by analyzing spectral lines. Techniques like prism dispersion and later spectroscopes made these insights possible.\"},{\"question\":\"What did the Balmer and Ritz formulas accomplish?\",\"answer\":\"They provided empirical ways to fit hydrogen’s emission wavelengths across spectral regions. Ritz’s modification unified line spectra using a single constant, guiding later theory development.\"},{\"question\":\"Why did Planck’s and Einstein’s work matter for the development of quantum theory?\",\"answer\":\"Planck derived the blackbody radiation spectrum by assuming energy is quantized as multiples of hν. Einstein used the same quantum idea to explain the photoelectric effect, showing that light energy is absorbed in quanta (photons).\"}]","The quantum mechanics of atoms and molecules - Introduction | PDF",1789975987,7752]