{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42846,"title":"Wien's displacement law","description":"Given the black body temperature (in *Celsius*), output the weavelength (in *meters*) at which the radiation peaks, according to \u003chttps://en.wikipedia.org/wiki/Wien's_displacement_law Wien's Displacement Law\u003e.\r\n\r\nTo convert Celsius into Kelvin, use 273.15.","description_html":"\u003cp\u003eGiven the black body temperature (in \u003cb\u003eCelsius\u003c/b\u003e), output the weavelength (in \u003cb\u003emeters\u003c/b\u003e) at which the radiation peaks, according to \u003ca href = \"https://en.wikipedia.org/wiki/Wien's_displacement_law\"\u003eWien's Displacement Law\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eTo convert Celsius into Kelvin, use 273.15.\u003c/p\u003e","function_template":"function lambda = WienWavelength(T)\r\n   h  = 6.62607004081e-34; % Planck's constant [W]\r\n   c  = 299792458;         % Speed of light [m/s]\r\n   R  = 8.314459848;       % Gas constant [J/K/mol]\r\n   Na = 6.02214085774e23;  % Avogadro constant [1/mol]\r\n   kb = R/Na;              % Boltzmann constant [J/K]\r\n   x  = 4.965114231744276; % 5+lambertw(-5*exp(-5)); % Solution for Planck's law with wavelength.\r\n   b  = [];\r\n   lambda = [];\r\nend","test_suite":"%%\r\nT = 1;\r\nlambda_correct = 1.057002706519664e-05;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 10;\r\nlambda_correct = 1.023405587117661e-05;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 100;\r\nlambda_correct = 7.765705265774241e-06;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 1000;\r\nlambda_correct = 2.276065601008253e-06;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2016-05-05T13:22:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-05-05T12:13:29.000Z","updated_at":"2026-02-10T11:24:06.000Z","published_at":"2016-05-05T13:22:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the black body temperature (in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCelsius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), output the weavelength (in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emeters\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) at which the radiation peaks, according to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Wien's_displacement_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWien's Displacement Law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo convert Celsius into Kelvin, use 273.15.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":42846,"title":"Wien's displacement law","description":"Given the black body temperature (in *Celsius*), output the weavelength (in *meters*) at which the radiation peaks, according to \u003chttps://en.wikipedia.org/wiki/Wien's_displacement_law Wien's Displacement Law\u003e.\r\n\r\nTo convert Celsius into Kelvin, use 273.15.","description_html":"\u003cp\u003eGiven the black body temperature (in \u003cb\u003eCelsius\u003c/b\u003e), output the weavelength (in \u003cb\u003emeters\u003c/b\u003e) at which the radiation peaks, according to \u003ca href = \"https://en.wikipedia.org/wiki/Wien's_displacement_law\"\u003eWien's Displacement Law\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eTo convert Celsius into Kelvin, use 273.15.\u003c/p\u003e","function_template":"function lambda = WienWavelength(T)\r\n   h  = 6.62607004081e-34; % Planck's constant [W]\r\n   c  = 299792458;         % Speed of light [m/s]\r\n   R  = 8.314459848;       % Gas constant [J/K/mol]\r\n   Na = 6.02214085774e23;  % Avogadro constant [1/mol]\r\n   kb = R/Na;              % Boltzmann constant [J/K]\r\n   x  = 4.965114231744276; % 5+lambertw(-5*exp(-5)); % Solution for Planck's law with wavelength.\r\n   b  = [];\r\n   lambda = [];\r\nend","test_suite":"%%\r\nT = 1;\r\nlambda_correct = 1.057002706519664e-05;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 10;\r\nlambda_correct = 1.023405587117661e-05;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 100;\r\nlambda_correct = 7.765705265774241e-06;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n\r\n%%\r\nT = 1000;\r\nlambda_correct = 2.276065601008253e-06;\r\nassert(abs(WienWavelength(T)/lambda_correct-1)\u003c1e-5);\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2016-05-05T13:22:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-05-05T12:13:29.000Z","updated_at":"2026-02-10T11:24:06.000Z","published_at":"2016-05-05T13:22:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the black body temperature (in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCelsius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), output the weavelength (in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emeters\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) at which the radiation peaks, according to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Wien's_displacement_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWien's Displacement Law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo convert Celsius into Kelvin, use 273.15.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[],[{"value":"easy","count":1,"selected":false}]],"term":"tag:\"wave\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}