{"id":37632,"date":"2025-06-26T03:36:59","date_gmt":"2025-06-26T03:36:59","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37632"},"modified":"2025-06-26T03:37:01","modified_gmt":"2025-06-26T03:37:01","slug":"if-light-has-a-wavelength-of-585-nm-what-is-the-energy-of-this-light-expressed-with-units-of-kj-mol","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/if-light-has-a-wavelength-of-585-nm-what-is-the-energy-of-this-light-expressed-with-units-of-kj-mol\/","title":{"rendered":"If light has a wavelength of 585 nm, what is the energy of this light expressed with units of kJ\/mol"},"content":{"rendered":"\n<p>If light has a wavelength of 585 nm, what is the energy of this light expressed with units of kJ\/mol? A beam of radiation has an energy of 3.11\u00c3\u201410^2 kJ\/mol. What is the wavelength of this light<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To answer both parts of this question, we\u2019ll use two key equations:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Energy of a photon:<\/h3>\n\n\n\n<p>E=hc\u03bbE = \\frac{hc}{\\lambda}E=\u03bbhc\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>EEE is the energy of a single photon (in joules),<\/li>\n\n\n\n<li>h=6.626\u00d710\u221234\u2009J\\cdotpsh = 6.626 \\times 10^{-34} \\, \\text{J\u00b7s}h=6.626\u00d710\u221234J\\cdotps is Planck\u2019s constant,<\/li>\n\n\n\n<li>c=3.00\u00d7108\u2009m\/sc = 3.00 \\times 10^8 \\, \\text{m\/s}c=3.00\u00d7108m\/s is the speed of light,<\/li>\n\n\n\n<li>\u03bb\\lambda\u03bb is the wavelength in meters.<\/li>\n<\/ul>\n\n\n\n<p>To find energy per mole of photons (kJ\/mol), we multiply the result by <strong>Avogadro\u2019s number<\/strong>:NA=6.022\u00d71023\u2009mol\u22121N_A = 6.022 \\times 10^{23} \\, \\text{mol}^{-1}NA\u200b=6.022\u00d71023mol\u22121<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part 1: Energy of light with wavelength 585 nm<\/strong><\/h3>\n\n\n\n<p>Convert 585 nm to meters:585\u2009nm=585\u00d710\u22129\u2009m585 \\, \\text{nm} = 585 \\times 10^{-9} \\, \\text{m}585nm=585\u00d710\u22129m<\/p>\n\n\n\n<p>Now plug into the equation:E=6.626\u00d710\u221234\u00d73.00\u00d7108585\u00d710\u22129=3.398\u00d710\u221219\u2009JE = \\frac{6.626 \\times 10^{-34} \\times 3.00 \\times 10^8}{585 \\times 10^{-9}} = 3.398 \\times 10^{-19} \\, \\text{J}E=585\u00d710\u221296.626\u00d710\u221234\u00d73.00\u00d7108\u200b=3.398\u00d710\u221219J<\/p>\n\n\n\n<p>Energy per mole:Emol=3.398\u00d710\u221219\u00d76.022\u00d71023=204.5\u2009kJ\/molE_{\\text{mol}} = 3.398 \\times 10^{-19} \\times 6.022 \\times 10^{23} = 204.5 \\, \\text{kJ\/mol}Emol\u200b=3.398\u00d710\u221219\u00d76.022\u00d71023=204.5kJ\/mol<\/p>\n\n\n\n<p><strong>Answer: 204.5 kJ\/mol<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part 2: Wavelength of light with energy 311 kJ\/mol<\/strong><\/h3>\n\n\n\n<p>Convert kJ\/mol to J per photon:311\u00d71036.022\u00d71023=5.164\u00d710\u221219\u2009J\\frac{311 \\times 10^3}{6.022 \\times 10^{23}} = 5.164 \\times 10^{-19} \\, \\text{J}6.022\u00d71023311\u00d7103\u200b=5.164\u00d710\u221219J<\/p>\n\n\n\n<p>Use the photon energy formula solved for \u03bb\\lambda\u03bb:\u03bb=hcE=6.626\u00d710\u221234\u00d73.00\u00d71085.164\u00d710\u221219=3.85\u00d710\u22127\u2009m\\lambda = \\frac{hc}{E} = \\frac{6.626 \\times 10^{-34} \\times 3.00 \\times 10^8}{5.164 \\times 10^{-19}} = 3.85 \\times 10^{-7} \\, \\text{m}\u03bb=Ehc\u200b=5.164\u00d710\u2212196.626\u00d710\u221234\u00d73.00\u00d7108\u200b=3.85\u00d710\u22127m<\/p>\n\n\n\n<p>Convert to nanometers:3.85\u00d710\u22127\u2009m=385\u2009nm3.85 \\times 10^{-7} \\, \\text{m} = 385 \\, \\text{nm}3.85\u00d710\u22127m=385nm<\/p>\n\n\n\n<p><strong>Answer: 385 nm<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The energy of light is inversely related to its wavelength. This means that shorter wavelengths carry more energy per photon, while longer wavelengths carry less. To compute the energy of light from its wavelength, we use the equation E=hc\/\u03bbE = hc\/\\lambdaE=hc\/\u03bb, where hhh is Planck\u2019s constant and ccc is the speed of light. These two constants allow us to convert a light wave\u2019s length into the energy associated with a single photon.<\/p>\n\n\n\n<p>In the first part, we converted the given wavelength of 585 nm into meters and calculated the energy of one photon. Since chemists typically work with moles, we scaled this energy up by multiplying by Avogadro\u2019s number, giving us the energy per mole of photons, which came out to approximately 204.5 kJ\/mol.<\/p>\n\n\n\n<p>In the second part, we worked the process in reverse. Given the energy in kJ\/mol, we first converted this to joules per photon by dividing by Avogadro\u2019s number. With that energy per photon, we then rearranged the same formula to solve for wavelength. The result was 385 nm, which lies in the visible light spectrum, close to violet.<\/p>\n\n\n\n<p>These relationships between energy, wavelength, and frequency help explain various phenomena in chemistry and physics, from how molecules absorb light to how solar panels generate electricity. Understanding these conversions is fundamental in spectroscopy and photochemistry.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-937.jpeg\" alt=\"\" class=\"wp-image-37633\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-937.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-937-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-937-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If light has a wavelength of 585 nm, what is the energy of this light expressed with units of kJ\/mol? A beam of radiation has an energy of 3.11\u00c3\u201410^2 kJ\/mol. What is the wavelength of this light The Correct Answer and Explanation is: To answer both parts of this question, we\u2019ll use two key equations: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37632","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37632"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37632\/revisions"}],"predecessor-version":[{"id":37634,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37632\/revisions\/37634"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}