{"id":307,"date":"2012-11-15T18:14:58","date_gmt":"2012-11-15T18:14:58","guid":{"rendered":"http:\/\/pages.charlotte.edu\/vasily-astratov\/?page_id=307"},"modified":"2013-04-05T18:19:44","modified_gmt":"2013-04-05T18:19:44","slug":"opti-61058105-take-home-exam","status":"publish","type":"page","link":"http:\/\/pages.charlotte.edu\/vasily-astratov\/courses\/opti-61058105-optical-properties-of-materials-i\/opti-61058105-take-home-exam\/","title":{"rendered":"OPTI 6105\/8105: Take Home Exam"},"content":{"rendered":"<p align=\"center\">Take Home Exam<br \/>\nOPTI 6105\/8105<br \/>\n3\/22\/2005<\/p>\n<p align=\"center\">(60 pts Total)<\/p>\n<p style=\"text-align: left;\" align=\"center\">Instructions:<\/p>\n<ul>\n<li>This is an open book, open note take home exam.<\/li>\n<li>Contact me if you need clarification on any question.<\/li>\n<li>Email:\u00a0<a href=\"mailto:astratov@uncc.edu\">astratov@uncc.edu<\/a>.\u00a0\u00a0If you cannot contact me, make any assumption you feel are necessary and work the problem.\u00a0\u00a0State your assumption clearly so I can follow what you did.<\/li>\n<li>The exam must be turned in by 5pm on Friday, 3\/25\/2004.\u00a0\u00a0Please place it under my door (Room 141\u00a0Burson).<\/li>\n<\/ul>\n<p style=\"text-align: center;\">THIS EXAM IS TO ASSESS\u00a0<strong><span style=\"text-decoration: underline;\">YOUR<\/span><\/strong>\u00a0UNDERSTANDING OF THE MATERIAL.<br \/>\nDO YOUR OWN WORK.<br \/>\nDO NOT WORK TOGETHER ON THIS EXAM.<\/p>\n<p style=\"text-align: center;\" align=\"center\">If you find relevant information in a book, on the internet, etc.,<br \/>\ndo not plagiarize (copy the text word for word).<\/p>\n<p align=\"center\"><span style=\"text-decoration: underline;\">YOUR ANSWERS MUST BE IN YOUR OWN WORDS.<\/span><\/p>\n<p align=\"center\"><span style=\"text-decoration: underline;\">VIOLATION OF THESE INSTRUCTIONS WILL BE CONSIDERED CHEATING AND WILL BE DELT WITH ACCORDING TO THE UNIVERSITY CODE OF ACADEMIC INTEGRITY (SEE SYLLABUS)<\/span><\/p>\n<p style=\"text-align: left;\" align=\"center\">1. Fox, Ch.1: 1.15 (10 pts)<br \/>\n2. Fox, Ch.2:\u00a0\u00a02.2\u00a0\u00a0(10 pts)<br \/>\n3. Fox, Ch.2:\u00a0\u00a02.7\u00a0\u00a0(10 pts)<br \/>\n4. Fox, Ch.7:\u00a0\u00a07.5\u00a0\u00a0(10 pts)<\/p>\n<p>Additional problem (20 pts)<br \/>\n5.\u00a0\u00a0Along a crystal axis in a\u00a0NaCl\u00a0crystal, the potential energy that holds the ionic crystal together is well described by the equation,<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-content\/uploads\/sites\/152\/2012\/11\/image0021.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-308 aligncenter\" title=\"image002\" src=\"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-content\/uploads\/sites\/152\/2012\/11\/image0021.gif\" alt=\"\" width=\"156\" height=\"48\" \/><\/a><\/p>\n<p>where\u00a0<strong><em>x<\/em><\/strong>\u00a0is the separation distance of the Na<sup>+<\/sup>\u00a0and\u00a0Cl<sup>&#8211;<\/sup>\u00a0ions.\u00a0\u00a0The first term captures the net electrostatic attraction between the ions, and the second term provides a repulsion that keeps the ions from getting too close. The constant\u00a0<strong><em>a<\/em><\/strong>\u00a0is called theMadelung\u00a0constant and it sets the strength of the attractive term. The\u00a0Madelung\u00a0constant for\u00a0NaCl\u00a0is 1.7476.\u00a0\u00a0The equilibrium separation between ions in\u00a0NaCl\u00a0is 0.281 nm and this occurs where the potential energy is a minimum.\u00a0\u00a0For most ionic solids, the value of\u00a0<strong><em>n<\/em><\/strong>\u00a0is between 8 and 10 and is approximately 8 for\u00a0NaCl.<\/p>\n<p>(a)\u00a0\u00a0Using the equilibrium condition, derive an expression that can be used to determine the value of the constant\u00a0<strong><em>A<\/em><\/strong>.<\/p>\n<p>(b)\u00a0\u00a0Determine the value of\u00a0<strong><em>A<\/em><\/strong>.\u00a0\u00a0Use nanometer for the unit of length rather than meter.<\/p>\n<p>(c)\u00a0\u00a0For small displacements from equilibrium, the restoring force is well described by\u00a0Hooke\u2019s\u00a0Law.\u00a0\u00a0Carry out a\u00a0Taylor\u00a0series expansion of the potential function about the equilibrium point in this limit.<\/p>\n<p>(d)\u00a0\u00a0Estimate the value of the effective spring constant for small changes in the\u00a0NaCl\u00a0bond length.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Take Home Exam OPTI 6105\/8105 3\/22\/2005 (60 pts Total) Instructions: This is an open book, open note take home exam. Contact me if you need clarification on any question. Email:\u00a0astratov@uncc.edu.\u00a0\u00a0If you cannot contact me, make any assumption you feel are necessary and work the problem.\u00a0\u00a0State your assumption clearly so I can follow what you did. [&hellip;]<\/p>\n","protected":false},"author":684,"featured_media":0,"parent":57,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-no-sidebar.php","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-307","page","type-page","status-publish","hentry"],"jetpack_shortlink":"https:\/\/wp.me\/P2TGes-4X","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/pages\/307","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/users\/684"}],"replies":[{"embeddable":true,"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/comments?post=307"}],"version-history":[{"count":9,"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/pages\/307\/revisions"}],"predecessor-version":[{"id":573,"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/pages\/307\/revisions\/573"}],"up":[{"embeddable":true,"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/pages\/57"}],"wp:attachment":[{"href":"http:\/\/pages.charlotte.edu\/vasily-astratov\/wp-json\/wp\/v2\/media?parent=307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}