[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-650801-105":59,"doc-detail-650801-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","shape-of-atomic-orbitals-spd-overview-of-s-p-and-d-orbitals","Shape of Atomic Orbitals (s,p,d) - Overview of s-, p-, and d-Orbitals","","Wave mechanical modeling of atoms describes electrons as having non-zero probability density across space, with meaningful regions excluding angular and radial nodes. The excerpt explains that orbital shapes in primitive diagrams represent the region covering about 90–95% probability density, built by plotting radial wave functions and superimposing angular parts. It then outlines s-orbitals as spherical clouds without radial nodes, p-orbitals with sign changes across the xy-plane producing characteristic lobes, and d-orbitals with nodal conical surfaces and alternating sign regions along principal axes.",{"@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/shape-of-atomic-orbitals-spd-overview-of-s-p-and-d-orbitals/650801/",{"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/shape-of-atomic-orbitals-spd-overview-of-s-p-and-d-orbitals/650801.png","ImageObject",300,407,{"name":92,"@type":93},"River Wang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-24",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How are atomic orbital shapes constructed in the wave mechanical model?","Question",{"text":112,"@type":113},"The excerpt states that one first plots the radial wave function, then superimposes the angular part to obtain the full orbital shape.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What defines the shape of an s-orbital in this description?",{"text":117,"@type":113},"The radial part has the largest magnitude at r=0 and decreases outward, while the angular part leads to a spherical cloud with no radial node.",{"name":119,"@type":110,"acceptedAnswer":120},"How do p- and d-orbitals differ in terms of sign and nodes?",{"text":121,"@type":113},"p-orbitals change sign across the xy-plane, giving positive values above and negative values below. d-orbitals can become completely zero on two conical surfaces before changing sign in different lobes.","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},650801,1793025737,{"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":39,"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},1099514067438,"https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542","# ※Shape of Atomic Orbitals (s,p&d)\n\nThe wave mechanical model of atom says that there is a non-zero probability of finding the electronalmost everywhere in space excepting the angular and radial nodes.This means that primitive diagrams thatdepict the orbital shapes are intended to describe the region encompassing 90-95%probability density.In atypical drawing of orbital,we first plot the radial wave function and the angular part is superimposed.Theshapes of some typical orbitals are discussed below.  \n# Shape ofs-Orbitals\n\nIn order to draw the shape of s-orbital,we first need to recall the radial part of the same and then wewill have to superimpose the angular part.For instance,the radial part of 1s orbital is  \n(443)  \nIt is obvious from the equation(443)that the radial part of the wave function has the largest magnitude whenr=0,and it decreases as we move away from the nucleus.The function will become zero only at infinitedistance and will never change its sign.All this leads to a spherical-shaped cloud without any radial node.Theangular part of every s-orbital is  \n(444)  \nHence,after multiplying radial wave function by a constant value of the angular part,the magnitude of functionat all the points in space willreduce to 28%of the initial value.  \n1s  \n2s  \n3s  \nFigure 26.The shape of some lower energy s-orbitals.  \nSimilarly,the shapes of some other s-orbitals are also given below to explain the concept more precisely.It isworthy to mention that the plots are easy to draw if we treat radial and angular parts consequently.  \n# Shape ofp-Orbitals\n\nIn order to draw the shape of p-orbital,we first need to recall the radial part of the same and then wewill have to superimpose the angular part.For instance,the radial part of2p orbital is  \n(445)  \nIt is obvious from the equation(445)that the radial part of the wave function has the zero magnitudes when r=0;and it increases as we move away from the nucleus,reaches a maximum,and decreases afterward.Thefunction becomes zero only at infinite distance and will never change its sign.All this leads to a spherical-shaped cloud without any radial node.The angular part of p-orbitals are  \n(446)  \n(447)  \nHence,the full plot for p=-orbital is obtained after multiplying radial wave function by angular part given byequation (446);and the sign of function above the xy-plane will remain positive whereas a negative sign willbe obtained below xy-planei ISimilarly,wercanitobtain the three-dimensional plots for px and py by multiplyingequation(445)by equation(447).  Www.dalalinstitute.com  \n2py  \n2p₂  \n2px  \nFigure 27.The shape of 2p-orbitals.  \nSimilarly,the shapes of some other p-orbitals are also given below to explain the concept more precisely.It isworthy to mention that the plots are easy to draw if we treat radial and angular parts consequently.  \n3py  \n3px  \n5py  \n5px  \nFigure 28.The shape of some 3p,4pand 5p orbitals.  \n3p₂  \n5p₂  \n# Shape of d-Orbitals\n\nIn order to draw the shape of d-orbital,we first need to recall the radial part of the same and then wewill have to superimpose the angular part.For instance,the radial part of 3d orbital is  \n(448)  \nIt is obvious from the equation(448)that the radial part of the wave function has the zero magnitudes when r=0;and it increases as we move away from the nucleus,reaches a maximum,and decreases afterward.Thefunction becomes zero only at infinite distance and will never change its sign.All this leads to a spherical-shaped cloud without any radial node.The angular part of d-orbitals are  \n(449)  \n(450)  \n(451)  \nHence,the full plot for d²-orbital is obtained after multiplying radial wave function by angular part given byequation(449);and the sign of function in the xy-plane will become negative whereas a positive sign will beobtained intwo opposite lobes along z-axis.It is also worthy to note that the function becomes completely zeroin two conical surfaces (above and below)before changing its sign.Similarly,we can obtain the three-dimensional p","cbCaijQakoXR3m7P","https://ap.wps.com/l/cbCaijQakoXR3m7P","pdf",1264226,14,"English","# Shape of Atomic Orbitals (s,p&d)\n# Shape of s-Orbitals\n# Shape of p-Orbitals\n# Shape of d-Orbitals","[{\"question\":\"How are atomic orbital shapes constructed in the wave mechanical model?\",\"answer\":\"The excerpt states that one first plots the radial wave function, then superimposes the angular part to obtain the full orbital shape.\"},{\"question\":\"What defines the shape of an s-orbital in this description?\",\"answer\":\"The radial part has the largest magnitude at r=0 and decreases outward, while the angular part leads to a spherical cloud with no radial node.\"},{\"question\":\"How do p- and d-orbitals differ in terms of sign and nodes?\",\"answer\":\"p-orbitals change sign across the xy-plane, giving positive values above and negative values below. d-orbitals can become completely zero on two conical surfaces before changing sign in different lobes.\"}]","Shape of Atomic Orbitals (s,p,d) - Overview of s-, p-, and d-Orbitals | PDF",1792846084,35]