{"id":189229,"date":"2025-02-08T21:02:28","date_gmt":"2025-02-08T21:02:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189229"},"modified":"2025-02-08T21:02:30","modified_gmt":"2025-02-08T21:02:30","slug":"calculate-the-energy-in-kj-mol-of-light-with-a-wavelength-of-450-nm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/08\/calculate-the-energy-in-kj-mol-of-light-with-a-wavelength-of-450-nm\/","title":{"rendered":"Calculate the energy in kJ\/mol of light with a wavelength of 450 nm"},"content":{"rendered":"\n<p>Calculate the energy in kJ\/mol of light with a wavelength of 450 nm.\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 (h: 6,626&#215;10-34Js; c: 3x108ms-1; NA:\u00c3\u201a\u00c2 6,02&#215;1023\u00c3\u201a\u00c2 mol-1)<\/p>\n\n\n\n<p>\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>\u00c3\u201a\u00c2 A<br>4.42\u00c3\u0192\u00e2\u20ac\u201d10-19\u00c3\u201a\u00c2 kJ\/mol<\/p>\n\n\n\n<p>B \u00c3\u201a\u00c2<br>266 kJ\/mol\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2<\/p>\n\n\n\n<p>C \u00c3\u201a\u00c2<br>6.63\u00c3\u0192\u00e2\u20ac\u201d103\u00c3\u201a\u00c2 kJ\/mol<\/p>\n\n\n\n<p>D \u00c3\u201a\u00c2<br>4.42\u00c3\u0192\u00e2\u20ac\u201d10-22\u00c3\u201a\u00c2 kJ\/mol\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2<\/p>\n\n\n\n<p>E \u00c3\u201a\u00c2<br>0.266 kJ\/mol<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the energy of light in kJ\/mol, we can use the following formula:<\/p>\n\n\n\n<p>[<br>E = \\dfrac{hc}{\\lambda}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(E) is the energy of one photon (in joules),<\/li>\n\n\n\n<li>(h) is Planck&#8217;s constant ((6.626 \\times 10^{-34}) J\u00b7s),<\/li>\n\n\n\n<li>(c) is the speed of light ((3.0 \\times 10^8) m\/s),<\/li>\n\n\n\n<li>(\\lambda) is the wavelength of the light (in meters).<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 1: Convert the wavelength to meters.<\/strong><br>Given that the wavelength is 450 nm (nanometers), we convert it to meters:<br>[<br>450 \\, \\text{nm} = 450 \\times 10^{-9} \\, \\text{m}<br>]<\/p>\n\n\n\n<p><strong>Step 2: Calculate the energy per photon in joules.<\/strong><br>Substitute the known values into the equation:<br>[<br>E = \\dfrac{(6.626 \\times 10^{-34} \\, \\text{J\u00b7s}) \\times (3.0 \\times 10^8 \\, \\text{m\/s})}{450 \\times 10^{-9} \\, \\text{m}}<br>]<br>[<br>E = \\dfrac{1.9878 \\times 10^{-25}}{450 \\times 10^{-9}} = 4.42 \\times 10^{-19} \\, \\text{J}<br>]<\/p>\n\n\n\n<p><strong>Step 3: Convert energy per photon to energy per mole.<\/strong><br>To find the energy per mole, multiply by Avogadro&#8217;s number ((N_A = 6.02 \\times 10^{23} \\, \\text{mol}^{-1})):<br>[<br>E_{\\text{mol}} = (4.42 \\times 10^{-19} \\, \\text{J}) \\times (6.02 \\times 10^{23} \\, \\text{mol}^{-1})<br>]<br>[<br>E_{\\text{mol}} = 2.66 \\times 10^5 \\, \\text{J\/mol}<br>]<\/p>\n\n\n\n<p><strong>Step 4: Convert to kJ\/mol.<\/strong><br>Since 1 kJ = 1000 J:<br>[<br>E_{\\text{mol}} = \\dfrac{2.66 \\times 10^5 \\, \\text{J\/mol}}{1000} = 266 \\, \\text{kJ\/mol}<br>]<\/p>\n\n\n\n<p><strong>Final Answer:<\/strong><br>The correct answer is <strong>B) 266 kJ\/mol<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This process demonstrates how to calculate the energy of light using the energy formula for photons. First, the wavelength is converted to meters. Next, the energy of a single photon is calculated using the constants of Planck&#8217;s constant and the speed of light. Finally, the energy is converted from joules per photon to joules per mole by multiplying with Avogadro\u2019s number. The conversion to kJ\/mol gives the energy in more convenient units for chemistry applications.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the energy in kJ\/mol of light with a wavelength of 450 nm.\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 (h: 6,626&#215;10-34Js; c: 3x108ms-1; NA:\u00c3\u201a\u00c2 6,02&#215;1023\u00c3\u201a\u00c2 mol-1) \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 A4.42\u00c3\u0192\u00e2\u20ac\u201d10-19\u00c3\u201a\u00c2 kJ\/mol B \u00c3\u201a\u00c2266 kJ\/mol\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 C \u00c3\u201a\u00c26.63\u00c3\u0192\u00e2\u20ac\u201d103\u00c3\u201a\u00c2 kJ\/mol D \u00c3\u201a\u00c24.42\u00c3\u0192\u00e2\u20ac\u201d10-22\u00c3\u201a\u00c2 kJ\/mol\u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 \u00c3\u201a\u00c2 E \u00c3\u201a\u00c20.266 kJ\/mol The Correct Answer and Explanation is : To calculate [&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 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