To calculate the density<\/strong> of aluminum, we use the following formula:<\/p>\n\n\n\n [ Aluminum crystallizes in a face-centered cubic (FCC) unit cell<\/strong>. The number of atoms per unit cell in an FCC structure is 4<\/strong>.<\/p>\n\n\n\n The atomic mass of aluminum is 26.98 g\/mol<\/strong>, and Avogadro\u2019s number<\/strong> is:<\/p>\n\n\n\n [ The mass of one<\/strong> aluminum atom:<\/p>\n\n\n\n [ Since the unit cell contains 4 atoms<\/strong>:<\/p>\n\n\n\n [ [ In an FCC structure, the edge length (a)<\/strong> is related to the atomic radius (( r )) by:<\/p>\n\n\n\n [ Given ( r = 143 ) pm<\/strong> ( = 143 \\times 10^{-12} ) m:<\/p>\n\n\n\n [ [ [ The volume<\/strong> of the unit cell:<\/p>\n\n\n\n [ [ [ [ [ [ The density of aluminum is<\/strong> ( 2.70 ) g\/cm\u00b3<\/strong>.<\/p>\n\n\n\n Here is the 3D diagram of the face-centered cubic (FCC) unit cell structure of aluminum. It illustrates the atomic arrangement, including the atomic radius (143 pm) and edge length (a). <\/p>\n","protected":false},"excerpt":{"rendered":" Aluminum (atomic mass 26.98 g\/mol) crystallizes in a face-centered cubic unit cell. in addition, aluminum has an atomic radius of 143 pm. what is the density of aluminum? The correct answer and explanation is : To calculate the density of aluminum, we use the following formula: [\\text{Density} = \\frac{\\text{Mass of unit cell}}{\\text{Volume of unit cell}}] […]<\/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-198637","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198637","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=198637"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198637\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{Density} = \\frac{\\text{Mass of unit cell}}{\\text{Volume of unit cell}}
]<\/p>\n\n\n\nStep 1: Determine the number of atoms per unit cell<\/h3>\n\n\n\n
Step 2: Calculate the mass of the unit cell<\/h3>\n\n\n\n
N_A = 6.022 \\times 10^{23} \\text{ atoms\/mol}
]<\/p>\n\n\n\n
\\frac{26.98 \\text{ g\/mol}}{6.022 \\times 10^{23} \\text{ atoms\/mol}} = 4.48 \\times 10^{-23} \\text{ g}
]<\/p>\n\n\n\n
\\text{Mass of unit cell} = 4 \\times (4.48 \\times 10^{-23} \\text{ g})
]<\/p>\n\n\n\n
= 1.792 \\times 10^{-22} \\text{ g}
]<\/p>\n\n\n\nStep 3: Calculate the volume of the unit cell<\/h3>\n\n\n\n
a = \\frac{4r}{\\sqrt{2}}
]<\/p>\n\n\n\n
a = \\frac{4 \\times (143 \\times 10^{-12} \\text{ m})}{\\sqrt{2}}
]<\/p>\n\n\n\n
= \\frac{572 \\times 10^{-12}}{1.414}
]<\/p>\n\n\n\n
= 4.05 \\times 10^{-10} \\text{ m}
]<\/p>\n\n\n\n
V = a^3 = (4.05 \\times 10^{-10} \\text{ m})^3
]<\/p>\n\n\n\n
= 6.64 \\times 10^{-29} \\text{ m}^3
]<\/p>\n\n\n\nStep 4: Calculate the density<\/h3>\n\n\n\n
\\text{Density} = \\frac{\\text{Mass of unit cell}}{\\text{Volume of unit cell}}
]<\/p>\n\n\n\n
= \\frac{1.792 \\times 10^{-22} \\text{ g}}{6.64 \\times 10^{-29} \\text{ m}^3}
]<\/p>\n\n\n\n
= 2.70 \\times 10^3 \\text{ kg\/m}^3
]<\/p>\n\n\n\n
= 2.70 \\text{ g\/cm}^3
]<\/p>\n\n\n\nAnswer:<\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-747.png\")
<\/figure>\n\n\n\n