{"id":239825,"date":"2025-07-03T05:15:40","date_gmt":"2025-07-03T05:15:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=239825"},"modified":"2025-07-03T05:15:43","modified_gmt":"2025-07-03T05:15:43","slug":"atomic-packing-factor-apf-for-sc","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/atomic-packing-factor-apf-for-sc\/","title":{"rendered":"Atomic packing factor (APF) for SC."},"content":{"rendered":"\n<p>Atomic packing factor (APF) for SC. 0.52.a O 0.74.b O 0.68.c O 0.93.d O<\/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\/image-21.png\" alt=\"\" class=\"wp-image-239826\"\/><\/figure>\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 for the atomic packing factor (APF) of Simple Cubic (SC) is <strong>0.52 (a)<\/strong>.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>The Atomic Packing Factor (APF) is a measure of how efficiently the atoms are packed into a structure. It is calculated as the ratio of the volume occupied by atoms in the unit cell to the total volume of the unit cell.<\/p>\n\n\n\n<p>In a simple cubic (SC) structure:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Each unit cell has 1 atom.<\/li>\n\n\n\n<li>The atoms touch each other along the edges of the unit cell.<\/li>\n\n\n\n<li>The atoms are positioned at the corners of the cube.<\/li>\n<\/ul>\n\n\n\n<p>To calculate the APF for SC:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The volume of the unit cell is a3a^3a3, where &#8220;a&#8221; is the edge length of the unit cell.<\/li>\n\n\n\n<li>The number of atoms per unit cell is 1.<\/li>\n\n\n\n<li>The volume occupied by each atom is the volume of a sphere with radius rrr, and the formula for the volume of a sphere is 43\u03c0r3\\frac{4}{3} \\pi r^334\u200b\u03c0r3.<\/li>\n\n\n\n<li>In an SC structure, the edge length aaa is equal to 2 times the atomic radius rrr, i.e., a=2ra = 2ra=2r.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the APF for SC is calculated as:APF=Volume&nbsp;occupied&nbsp;by&nbsp;atoms&nbsp;in&nbsp;the&nbsp;unit&nbsp;cellTotal&nbsp;volume&nbsp;of&nbsp;the&nbsp;unit&nbsp;cell=43\u03c0r3a3=43\u03c0r3(2r)3=16\u03c0\u22480.52APF = \\frac{\\text{Volume occupied by atoms in the unit cell}}{\\text{Total volume of the unit cell}} = \\frac{\\frac{4}{3} \\pi r^3}{a^3} = \\frac{\\frac{4}{3} \\pi r^3}{(2r)^3} = \\frac{1}{6} \\pi \\approx 0.52APF=Total&nbsp;volume&nbsp;of&nbsp;the&nbsp;unit&nbsp;cellVolume&nbsp;occupied&nbsp;by&nbsp;atoms&nbsp;in&nbsp;the&nbsp;unit&nbsp;cell\u200b=a334\u200b\u03c0r3\u200b=(2r)334\u200b\u03c0r3\u200b=61\u200b\u03c0\u22480.52<\/p>\n\n\n\n<p>Therefore, the correct APF for Simple Cubic (SC) is <strong>0.52<\/strong>.<\/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-banner5-73.jpeg\" alt=\"\" class=\"wp-image-239827\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Atomic packing factor (APF) for SC. 0.52.a O 0.74.b O 0.68.c O 0.93.d O The Correct Answer and Explanation is: The correct answer for the atomic packing factor (APF) of Simple Cubic (SC) is 0.52 (a). Explanation: The Atomic Packing Factor (APF) is a measure of how efficiently the atoms are packed into a structure. [&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-239825","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/239825","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=239825"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/239825\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=239825"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=239825"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=239825"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}