{"id":245658,"date":"2025-07-06T10:42:16","date_gmt":"2025-07-06T10:42:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245658"},"modified":"2025-07-06T10:42:19","modified_gmt":"2025-07-06T10:42:19","slug":"the-sales-force-of-dunder-mifflin-consists-of-7-salespeople-who-work-in-the-scranton-office-and-11-who-work-in-the-stamford-office","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/the-sales-force-of-dunder-mifflin-consists-of-7-salespeople-who-work-in-the-scranton-office-and-11-who-work-in-the-stamford-office\/","title":{"rendered":"The sales force of Dunder Mifflin consists of 7 salespeople who work in the Scranton office and 11 who work in the Stamford office."},"content":{"rendered":"\n
The sales force of Dunder Mifflin consists of 7 salespeople who work in the Scranton office and 11 who work in the Stamford office. A production unit of 3 people is set up at random. What is the probability that it will include at least one salesperson who works in the Stamford office? The probability that the production unit will include of at least one salesperson who works in the Stamford office is (Type an integer or a fraction.)<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
1. Proposed Electron Configurations Correction:<\/h3>\n\n\n\n
Corrected electron configuration<\/strong>: Rubidium has an atomic number of 37, meaning it has 37 electrons. Following the Aufbau principle (filling orbitals from lowest to highest energy), the correct configuration is: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076 4s\u00b2 3d\u00b9\u2070 4p\u2076 5s\u00b2 4d\u00b9\u2070 5p\u2076 6s\u00b9<\/strong>
The outermost electron is in the 6s orbital<\/strong>.<\/li>
The configuration you provided starts filling 4d and 5f orbitals, which isn’t correct for Rubidium.<\/li><\/ul>Valence electrons<\/strong>: The valence electron is in the 6s orbital, so it is 6s\u00b9<\/strong>.<\/li>\n<\/ul>\n\n\n\n
Corrected electron configuration<\/strong>: Radium has an atomic number of 88, meaning it has 88 electrons. Following the Aufbau principle: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076 4s\u00b2 3d\u00b9\u2070 4p\u2076 5s\u00b2 4d\u00b9\u2070 5p\u2076 6s\u00b2 4f\u00b9\u2074 5d\u00b9\u2070 6p\u2076 7s\u00b2<\/strong>
The configuration provided has an error in how the d and f orbitals are filled.<\/li>
The 5f orbital is filled in the actinide series (starting with actinium), but Radium<\/strong> would have the 6s\u00b2 orbital<\/strong> as its highest energy orbital, not 5f\u00b2.<\/li><\/ul>Valence electrons<\/strong>: Radium has 2 valence electrons<\/strong> in the 7s orbital<\/strong>.<\/li>\n<\/ul>\n\n\n\n
2. Quantum Numbers and Orbital Sketches<\/h3>\n\n\n\n
a. The Outermost Electron of a Rubidium Ion (Rb\u207a)<\/h4>\n\n\n\n
\n
Electron configuration of Rb\u207a<\/strong>: Rubidium has an atomic number of 37. When it ionizes to form Rb\u207a<\/strong>, it loses one electron, resulting in 36 electrons. The electron configuration of Rb\u207a is: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076 4s\u00b2 3d\u00b9\u2070 4p\u2076 5s\u00b2 4d\u00b9\u2070 5p\u2076<\/strong> The outermost electron of the Rb\u207a ion<\/strong> is now in the 5s orbital<\/strong> (last filled orbital before ionization). Since Rubidium\u2019s valence electron is lost when forming the ion, there are no valence electrons in the ion. Quantum Numbers for the Outer Electron in Rb\u207a<\/strong>:
n<\/strong> = 5 (the principal quantum number)<\/li>
l<\/strong> = 0 (for an s orbital)<\/li>
m\u2097<\/strong> = 0 (since there\u2019s only one orientation for an s orbital)<\/li>
m\u209b<\/strong> = +\u00bd or -\u00bd (spin quantum number, can be either)<\/li><\/ul>Orbital Sketch<\/strong>: The 5s orbital<\/strong> is spherical, and it is drawn as a circle around the nucleus.<\/li>\n<\/ul>\n\n\n\n
b. The Electron Gained When an S Ion Becomes an S\u00b2 Ion<\/h4>\n\n\n\n
\n
For an S\u207b ion<\/strong> (atomic number 16, sulfur), the electron configuration is: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2074<\/strong> When it gains an electron to form S\u00b2\u207b<\/strong>, the configuration becomes: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076<\/strong> Quantum Numbers for the Gained Electron<\/strong>:
n<\/strong> = 3 (the principal quantum number)<\/li>
l<\/strong> = 1 (for a p orbital)<\/li>
m\u2097<\/strong> = -1, 0, or +1 (since p orbitals have three possible orientations)<\/li>
m\u209b<\/strong> = +\u00bd or -\u00bd (spin quantum number)<\/li><\/ul>Orbital Sketch<\/strong>: The 3p orbital<\/strong> has three lobes, oriented along the x, y, and z axes.<\/li>\n<\/ul>\n\n\n\n
c. The Electron Lost When an Ag Atom Ionizes<\/h4>\n\n\n\n
\n
Silver (Ag)<\/strong> has an atomic number of 47, and its electron configuration is: 1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076 4s\u00b2 3d\u00b9\u2070 4p\u2076 5s\u00b9 4d\u00b9\u2070<\/strong> When Ag<\/strong> ionizes to form Ag\u207a<\/strong>, it loses its 5s\u00b9 electron<\/strong>. Quantum Numbers for the Lost Electron<\/strong>:
n<\/strong> = 5 (the principal quantum number)<\/li>
l<\/strong> = 0 (for an s orbital)<\/li>
m\u2097<\/strong> = 0 (since there\u2019s only one orientation for an s orbital)<\/li>
m\u209b<\/strong> = +\u00bd or -\u00bd (spin quantum number)<\/li><\/ul>Orbital Sketch<\/strong>: The 5s orbital<\/strong> is spherical, and it is drawn as a circle around the nucleus.<\/li>\n<\/ul>\n\n\n\n\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
The sales force of Dunder Mifflin consists of 7 salespeople who work in the Scranton office and 11 who work in the Stamford office. A production unit of 3 people is set up at random. What is the probability that it will include at least one salesperson who works in the Stamford office? The probability […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-245658","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=245658"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245658\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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