{"id":264106,"date":"2025-07-21T11:07:02","date_gmt":"2025-07-21T11:07:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264106"},"modified":"2025-07-21T11:07:05","modified_gmt":"2025-07-21T11:07:05","slug":"which-of-the-following-is-not-a-valid-set-of-four-quantum-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/which-of-the-following-is-not-a-valid-set-of-four-quantum-numbers\/","title":{"rendered":"Which of the following is not a valid set of four quantum numbers"},"content":{"rendered":"\n<p>Which of the following is not a valid set of four quantum numbers? (n, l, m\u2081, m\u209b) a. 4, 0, 0, +1\/2 b. 2, 1, 0, -1\/2 c. 3, 2, -1, -1\/2 d. 1, 0, 0, +1\/2 e. 1, 1, 0, +1\/2<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>e. 1, 1, 0, +1\/2<\/strong>.<\/p>\n\n\n\n<p>Here\u2019s why:<\/p>\n\n\n\n<p>Quantum numbers describe the unique state of an electron in an atom. There are four quantum numbers:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Principal quantum number (n)<\/strong>: This represents the energy level of the electron. It must be a positive integer (1, 2, 3, \u2026).<\/li>\n\n\n\n<li><strong>Angular momentum quantum number (l)<\/strong>: This defines the shape of the orbital. It ranges from 0 to (n-1), where 0 corresponds to an s orbital, 1 corresponds to a p orbital, 2 corresponds to a d orbital, and so on.<\/li>\n\n\n\n<li><strong>Magnetic quantum number (m\u2081)<\/strong>: This specifies the orientation of the orbital in space. It can range from -l to +l, including 0.<\/li>\n\n\n\n<li><strong>Spin quantum number (m\u209b)<\/strong>: This describes the electron\u2019s spin, which can be either +1\/2 or -1\/2.<\/li>\n<\/ol>\n\n\n\n<p>Now, let\u2019s analyze each option:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option a (4, 0, 0, +1\/2)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>n = 4 (valid)<\/li>\n\n\n\n<li>l = 0 (valid because l ranges from 0 to n-1, so for n=4, l can be 0, 1, 2, or 3)<\/li>\n\n\n\n<li>m\u2081 = 0 (valid because m\u2081 can range from -l to +l, and since l=0, m\u2081 must be 0)<\/li>\n\n\n\n<li>m\u209b = +1\/2 (valid, spin can be either +1\/2 or -1\/2)<br><strong>This is a valid set of quantum numbers.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option b (2, 1, 0, -1\/2)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>n = 2 (valid)<\/li>\n\n\n\n<li>l = 1 (valid, l can be 0 or 1 when n=2)<\/li>\n\n\n\n<li>m\u2081 = 0 (valid, m\u2081 ranges from -l to +l, so m\u2081 can be -1, 0, or +1 for l=1)<\/li>\n\n\n\n<li>m\u209b = -1\/2 (valid)<br><strong>This is a valid set of quantum numbers.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option c (3, 2, -1, -1\/2)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>n = 3 (valid)<\/li>\n\n\n\n<li>l = 2 (valid, l can be 0, 1, or 2 when n=3)<\/li>\n\n\n\n<li>m\u2081 = -1 (valid, m\u2081 ranges from -l to +l, so m\u2081 can be -2, -1, 0, +1, +2 for l=2)<\/li>\n\n\n\n<li>m\u209b = -1\/2 (valid)<br><strong>This is a valid set of quantum numbers.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option d (1, 0, 0, +1\/2)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>n = 1 (valid)<\/li>\n\n\n\n<li>l = 0 (valid, l must be less than n, so for n=1, l=0)<\/li>\n\n\n\n<li>m\u2081 = 0 (valid, since l=0, m\u2081 must be 0)<\/li>\n\n\n\n<li>m\u209b = +1\/2 (valid)<br><strong>This is a valid set of quantum numbers.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option e (1, 1, 0, +1\/2)<\/strong>:\n<ul class=\"wp-block-list\">\n<li>n = 1 (valid)<\/li>\n\n\n\n<li>l = 1 (invalid because for n=1, l can only be 0)<\/li>\n\n\n\n<li>m\u2081 = 0 (this would be valid if l were 1, but l cannot be 1 when n=1)<\/li>\n\n\n\n<li>m\u209b = +1\/2 (valid)<br><strong>This is an invalid set of quantum numbers because l cannot be 1 when n=1.<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Thus, option <strong>e<\/strong> is the only invalid set.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1368.jpeg\" alt=\"\" class=\"wp-image-264108\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following is not a valid set of four quantum numbers? (n, l, m\u2081, m\u209b) a. 4, 0, 0, +1\/2 b. 2, 1, 0, -1\/2 c. 3, 2, -1, -1\/2 d. 1, 0, 0, +1\/2 e. 1, 1, 0, +1\/2 The Correct Answer and Explanation is: The correct answer is e. 1, 1, [&hellip;]<\/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-264106","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264106","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=264106"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264106\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}