Planar Density Expressions for BCC (100) and (110) Planes<\/strong><\/h3>\n\n\n\nPlanar Density Formula:<\/strong><\/h4>\n\n\n\nPlanar density (PD) is given by:<\/p>\n\n\n\n
[
PD = \\frac{\\text{Number of atoms centered on the plane}}{\\text{Area of the plane}}
]<\/p>\n\n\n\n
\n\n\n\n1. BCC (100) Plane<\/strong><\/h3>\n\n\n\n\n- In a BCC (Body-Centered Cubic) structure<\/strong>, each unit cell contains 2 atoms<\/strong>.<\/li>\n\n\n\n
- The (100) plane<\/strong> contains atoms at the four corners<\/strong> of a square.<\/li>\n\n\n\n
- Each corner atom contributes 1\/4th<\/strong> of an atom to the plane.<\/li>\n\n\n\n
- The central atom in the unit cell does not<\/strong> lie on this plane.<\/li>\n\n\n\n
- The lattice parameter<\/strong> (( a )) in terms of atomic radius (( R )) for a BCC structure is: [
a = \\frac{4R}{\\sqrt{3}}
]<\/li>\n\n\n\n- The area of the (100) plane<\/strong> is: [
A_{100} = a^2 = \\left(\\frac{4R}{\\sqrt{3}}\\right)^2 = \\frac{16R^2}{3}
]<\/li>\n\n\n\n- The number of atoms per (100) plane<\/strong>: [
N_{100} = 1 (4 \\times 1\/4)
]<\/li>\n\n\n\n- Planar Density for BCC (100) Plane:<\/strong> [
PD_{100} = \\frac{1}{\\frac{16R^2}{3}} = \\frac{3}{16R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n2. BCC (110) Plane<\/strong><\/h3>\n\n\n\n\n- The (110) plane<\/strong> contains atoms from two full corner atoms<\/strong> and one additional atom at the center<\/strong>.<\/li>\n\n\n\n
- The area of the (110) plane<\/strong> is: [
A_{110} = a \\times \\frac{a}{\\sqrt{2}} = \\frac{4R}{\\sqrt{3}} \\times \\frac{4R}{\\sqrt{3}\\sqrt{2}}
] [
A_{110} = \\frac{16R^2}{3\\sqrt{2}}
]<\/li>\n\n\n\n- The number of atoms per (110) plane<\/strong>: [
N_{110} = 2 \\times \\frac{1}{2} + 1 = 2
]<\/li>\n\n\n\n- Planar Density for BCC (110) Plane:<\/strong> [
PD_{110} = \\frac{2}{\\frac{16R^2}{3\\sqrt{2}}} = \\frac{3\\sqrt{2}}{8R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n(b) Compute and Compare Planar Density for Molybdenum<\/strong><\/h3>\n\n\n\n\n- Given atomic radius of Mo<\/strong>: ( R = 0.1363 ) nm.<\/li>\n<\/ul>\n\n\n\n
BCC (100) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
BCC (110) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1494.png\")
<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Planar density (PD) is given by:<\/p>\n\n\n\n
[
PD = \\frac{\\text{Number of atoms centered on the plane}}{\\text{Area of the plane}}
]<\/p>\n\n\n\n
\n\n\n\n
1. BCC (100) Plane<\/strong><\/h3>\n\n\n\n\n- In a BCC (Body-Centered Cubic) structure<\/strong>, each unit cell contains 2 atoms<\/strong>.<\/li>\n\n\n\n
- The (100) plane<\/strong> contains atoms at the four corners<\/strong> of a square.<\/li>\n\n\n\n
- Each corner atom contributes 1\/4th<\/strong> of an atom to the plane.<\/li>\n\n\n\n
- The central atom in the unit cell does not<\/strong> lie on this plane.<\/li>\n\n\n\n
- The lattice parameter<\/strong> (( a )) in terms of atomic radius (( R )) for a BCC structure is: [
a = \\frac{4R}{\\sqrt{3}}
]<\/li>\n\n\n\n- The area of the (100) plane<\/strong> is: [
A_{100} = a^2 = \\left(\\frac{4R}{\\sqrt{3}}\\right)^2 = \\frac{16R^2}{3}
]<\/li>\n\n\n\n- The number of atoms per (100) plane<\/strong>: [
N_{100} = 1 (4 \\times 1\/4)
]<\/li>\n\n\n\n- Planar Density for BCC (100) Plane:<\/strong> [
PD_{100} = \\frac{1}{\\frac{16R^2}{3}} = \\frac{3}{16R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n2. BCC (110) Plane<\/strong><\/h3>\n\n\n\n\n- The (110) plane<\/strong> contains atoms from two full corner atoms<\/strong> and one additional atom at the center<\/strong>.<\/li>\n\n\n\n
- The area of the (110) plane<\/strong> is: [
A_{110} = a \\times \\frac{a}{\\sqrt{2}} = \\frac{4R}{\\sqrt{3}} \\times \\frac{4R}{\\sqrt{3}\\sqrt{2}}
] [
A_{110} = \\frac{16R^2}{3\\sqrt{2}}
]<\/li>\n\n\n\n- The number of atoms per (110) plane<\/strong>: [
N_{110} = 2 \\times \\frac{1}{2} + 1 = 2
]<\/li>\n\n\n\n- Planar Density for BCC (110) Plane:<\/strong> [
PD_{110} = \\frac{2}{\\frac{16R^2}{3\\sqrt{2}}} = \\frac{3\\sqrt{2}}{8R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n(b) Compute and Compare Planar Density for Molybdenum<\/strong><\/h3>\n\n\n\n\n- Given atomic radius of Mo<\/strong>: ( R = 0.1363 ) nm.<\/li>\n<\/ul>\n\n\n\n
BCC (100) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
BCC (110) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
a = \\frac{4R}{\\sqrt{3}}
]<\/li>\n\n\n\n
A_{100} = a^2 = \\left(\\frac{4R}{\\sqrt{3}}\\right)^2 = \\frac{16R^2}{3}
]<\/li>\n\n\n\n
N_{100} = 1 (4 \\times 1\/4)
]<\/li>\n\n\n\n
PD_{100} = \\frac{1}{\\frac{16R^2}{3}} = \\frac{3}{16R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n
2. BCC (110) Plane<\/strong><\/h3>\n\n\n\n\n- The (110) plane<\/strong> contains atoms from two full corner atoms<\/strong> and one additional atom at the center<\/strong>.<\/li>\n\n\n\n
- The area of the (110) plane<\/strong> is: [
A_{110} = a \\times \\frac{a}{\\sqrt{2}} = \\frac{4R}{\\sqrt{3}} \\times \\frac{4R}{\\sqrt{3}\\sqrt{2}}
] [
A_{110} = \\frac{16R^2}{3\\sqrt{2}}
]<\/li>\n\n\n\n- The number of atoms per (110) plane<\/strong>: [
N_{110} = 2 \\times \\frac{1}{2} + 1 = 2
]<\/li>\n\n\n\n- Planar Density for BCC (110) Plane:<\/strong> [
PD_{110} = \\frac{2}{\\frac{16R^2}{3\\sqrt{2}}} = \\frac{3\\sqrt{2}}{8R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n(b) Compute and Compare Planar Density for Molybdenum<\/strong><\/h3>\n\n\n\n\n- Given atomic radius of Mo<\/strong>: ( R = 0.1363 ) nm.<\/li>\n<\/ul>\n\n\n\n
BCC (100) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
BCC (110) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
A_{110} = a \\times \\frac{a}{\\sqrt{2}} = \\frac{4R}{\\sqrt{3}} \\times \\frac{4R}{\\sqrt{3}\\sqrt{2}}
] [
A_{110} = \\frac{16R^2}{3\\sqrt{2}}
]<\/li>\n\n\n\n
N_{110} = 2 \\times \\frac{1}{2} + 1 = 2
]<\/li>\n\n\n\n
PD_{110} = \\frac{2}{\\frac{16R^2}{3\\sqrt{2}}} = \\frac{3\\sqrt{2}}{8R^2}
]<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n
(b) Compute and Compare Planar Density for Molybdenum<\/strong><\/h3>\n\n\n\n\n- Given atomic radius of Mo<\/strong>: ( R = 0.1363 ) nm.<\/li>\n<\/ul>\n\n\n\n
BCC (100) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
BCC (110) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
BCC (100) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
BCC (110) Plane:<\/strong><\/h4>\n\n\n\n[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
PD_{100} = \\frac{3}{16(0.1363)^2} = \\frac{3}{16(0.01858)}
]
[
PD_{100} = 10.11 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
[
PD_{110} = \\frac{3\\sqrt{2}}{8(0.1363)^2} = \\frac{3(1.414)}{8(0.01858)}
]
[
PD_{110} = 12.00 \\times 10^{18} \\text{ atoms\/m}^2
]<\/p>\n\n\n\n
Comparison:<\/strong><\/h3>\n\n\n\n\n- BCC (110) plane has a higher planar density<\/strong> than BCC (100) plane<\/strong>.<\/li>\n\n\n\n
- This indicates that (110) planes are more closely packed<\/strong> than (100) planes in BCC structures.<\/li>\n<\/ul>\n\n\n\n
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n<\/figure>\n\n\n\nThe image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Now, I will generate an image illustrating the (100) and (110) planes in a BCC structure.<\/p>\n\n\n\n The image illustrates the (100) and (110) planes in a Body-Centered Cubic (BCC) structure, showing their atomic arrangements and differences in planar density. Let me know if you need any modifications or additional explanations!<\/p>\n","protected":false},"excerpt":{"rendered":" derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum. The Correct Answer and Explanation is : Planar Density Expressions for BCC (100) and (110) Planes Planar Density Formula: Planar density (PD) is given by: [PD […]<\/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-194972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972","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=194972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/figure>\n\n\n\n