{"id":37629,"date":"2025-06-26T03:31:31","date_gmt":"2025-06-26T03:31:31","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37629"},"modified":"2025-06-26T03:31:32","modified_gmt":"2025-06-26T03:31:32","slug":"calculate-the-energy-in-kj-mol-of-light-with-a-wavelength-of-360-nm","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/calculate-the-energy-in-kj-mol-of-light-with-a-wavelength-of-360-nm\/","title":{"rendered":"Calculate the energy in kJ\/mol of light with a wavelength of 360 nm."},"content":{"rendered":"\n<p>Calculate the energy in kJ\/mol of light with a wavelength of 360 nm.<\/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 calculate the energy in kilojoules per mole (kJ\/mol) of light with a wavelength of 360 nm, we can use the following formula: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 (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 (speed of light)<\/li>\n\n\n\n<li>\u03bb=360\u2009nm=360\u00d710\u22129\u2009m\\lambda = 360 \\, \\text{nm} = 360 \\times 10^{-9} \\, \\text{m}\u03bb=360nm=360\u00d710\u22129m<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Energy of one photon<\/h3>\n\n\n\n<p>E=(6.626\u00d710\u221234)(3.00\u00d7108)360\u00d710\u22129=5.52\u00d710\u221219\u2009JE = \\frac{(6.626 \\times 10^{-34}) (3.00 \\times 10^8)}{360 \\times 10^{-9}} = 5.52 \\times 10^{-19} \\, \\text{J}E=360\u00d710\u22129(6.626\u00d710\u221234)(3.00\u00d7108)\u200b=5.52\u00d710\u221219J<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Convert to kJ\/mol<\/h3>\n\n\n\n<p>One mole of photons contains Avogadro\u2019s number of photons:6.022\u00d71023\u2009photons\/mol6.022 \\times 10^{23} \\, \\text{photons\/mol}6.022\u00d71023photons\/molEnergy&nbsp;per&nbsp;mole=(5.52\u00d710\u221219\u2009J)\u00d7(6.022\u00d71023)=3.32\u00d7105\u2009J\/mol\\text{Energy per mole} = (5.52 \\times 10^{-19} \\, \\text{J}) \\times (6.022 \\times 10^{23}) = 3.32 \\times 10^5 \\, \\text{J\/mol}Energy&nbsp;per&nbsp;mole=(5.52\u00d710\u221219J)\u00d7(6.022\u00d71023)=3.32\u00d7105J\/mol<\/p>\n\n\n\n<p>Convert joules to kilojoules:3.32\u00d7105\u2009J\/mol=332\u2009kJ\/mol3.32 \\times 10^5 \\, \\text{J\/mol} = 332 \\, \\text{kJ\/mol}3.32\u00d7105J\/mol=332kJ\/mol<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Final Answer: 332 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\">Explanation<\/h3>\n\n\n\n<p>Light behaves both like a wave and a particle. Each particle of light, known as a photon, carries a discrete amount of energy that depends on the wavelength. Shorter wavelengths correspond to higher energy photons, while longer wavelengths have lower energy.<\/p>\n\n\n\n<p>The energy of a photon is calculated using the equation E=hc\u03bbE = \\frac{hc}{\\lambda}E=\u03bbhc\u200b, where hhh is Planck\u2019s constant, ccc is the speed of light, and \u03bb\\lambda\u03bb is the wavelength. Because the wavelength in this question is given in nanometers, it must be converted to meters for consistency with the SI units used in the constants. Since 1 nanometer is equal to 1\u00d710\u221291 \\times 10^{-9}1\u00d710\u22129 meters, 360 nm becomes 3.60\u00d710\u221273.60 \\times 10^{-7}3.60\u00d710\u22127 meters.<\/p>\n\n\n\n<p>Using the formula, we find that a single photon of 360 nm light has an energy of approximately 5.52\u00d710\u2212195.52 \\times 10^{-19}5.52\u00d710\u221219 joules. While this value seems small, it is for just one photon. In chemistry, we are usually interested in the energy per mole, so we multiply the single-photon energy by Avogadro\u2019s number, 6.022\u00d710236.022 \\times 10^{23}6.022\u00d71023, to get the total energy in joules per mole. This gives about 3.32\u00d71053.32 \\times 10^53.32\u00d7105 joules per mole.<\/p>\n\n\n\n<p>Finally, we convert joules to kilojoules by dividing by 1000. This yields a final result of <strong>332 kilojoules per mole<\/strong>, which is a reasonable value for ultraviolet light. This energy is high enough to break chemical bonds, which is why UV light can cause damage to living tissues.<\/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-banner8-936.jpeg\" alt=\"\" class=\"wp-image-37630\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-936.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-936-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-936-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the energy in kJ\/mol of light with a wavelength of 360 nm. The Correct Answer and Explanation is: To calculate the energy in kilojoules per mole (kJ\/mol) of light with a wavelength of 360 nm, we can use the following formula:E=hc\u03bbE = \\frac{hc}{\\lambda}E=\u03bbhc\u200b Where: Step 1: Energy of one photon E=(6.626\u00d710\u221234)(3.00\u00d7108)360\u00d710\u22129=5.52\u00d710\u221219\u2009JE = \\frac{(6.626 \\times [&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-37629","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37629","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=37629"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37629\/revisions"}],"predecessor-version":[{"id":37631,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37629\/revisions\/37631"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37629"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}