{"id":224325,"date":"2025-06-03T04:12:12","date_gmt":"2025-06-03T04:12:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224325"},"modified":"2025-06-03T04:12:14","modified_gmt":"2025-06-03T04:12:14","slug":"a-photon-of-green-light-has-a-wavelength-of-520-nm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/a-photon-of-green-light-has-a-wavelength-of-520-nm\/","title":{"rendered":"A photon of green light has a wavelength of 520 nm"},"content":{"rendered":"\n<p>A photon of green light has a wavelength of 520 nm. Find the photon&#8217;s frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the frequency, momentum, and energy of a green light photon with a wavelength of 520 nm, we\u2019ll use fundamental equations from physics.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Wavelength, \u03bb=520\\lambda = 520 nm = 520\u00d710\u22129520 \\times 10^{-9} m<\/li>\n\n\n\n<li>Speed of light, c=3.00\u00d7108c = 3.00 \\times 10^8 m\/s<\/li>\n\n\n\n<li>Planck\u2019s constant, h=6.626\u00d710\u221234h = 6.626 \\times 10^{-34} J\u00b7s<\/li>\n\n\n\n<li>Electron charge, e=1.602\u00d710\u221219e = 1.602 \\times 10^{-19} C<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. Frequency ff:<\/strong><\/h3>\n\n\n\n<p>f=c\u03bb=3.00\u00d7108520\u00d710\u22129=5.77\u00d71014&nbsp;Hzf = \\frac{c}{\\lambda} = \\frac{3.00 \\times 10^8}{520 \\times 10^{-9}} = 5.77 \\times 10^{14} \\text{ Hz}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Momentum pp:<\/strong><\/h3>\n\n\n\n<p>p=h\u03bb=6.626\u00d710\u221234520\u00d710\u22129=1.274\u00d710\u221227&nbsp;kg\\cdotpm\/sp = \\frac{h}{\\lambda} = \\frac{6.626 \\times 10^{-34}}{520 \\times 10^{-9}} = 1.274 \\times 10^{-27} \\text{ kg\u00b7m\/s}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3. Energy EE:<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">In joules:<\/h4>\n\n\n\n<p>E=hf=(6.626\u00d710\u221234)(5.77\u00d71014)=3.821\u00d710\u221219&nbsp;JE = hf = (6.626 \\times 10^{-34})(5.77 \\times 10^{14}) = 3.821 \\times 10^{-19} \\text{ J}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">In electron volts (eV):<\/h4>\n\n\n\n<p>E=3.821\u00d710\u2212191.602\u00d710\u221219=2.38&nbsp;eVE = \\frac{3.821 \\times 10^{-19}}{1.602 \\times 10^{-19}} = 2.38 \\text{ eV}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation <\/strong><\/h3>\n\n\n\n<p>Light exhibits both wave-like and particle-like properties. A photon, the quantum particle of light, carries energy and momentum despite having no mass. To understand its behavior, we use the wave-particle duality framework. In this case, we are given the wavelength of a green light photon as 520 nm (nanometers), which falls within the visible spectrum.<\/p>\n\n\n\n<p>The <strong>frequency<\/strong> of the photon is calculated using the relation f=c\u03bbf = \\frac{c}{\\lambda}, where cc is the speed of light and \u03bb\\lambda is the wavelength. A shorter wavelength means a higher frequency, indicating more energetic photons. For 520 nm, the frequency turns out to be approximately 5.77\u00d710145.77 \\times 10^{14} Hz.<\/p>\n\n\n\n<p>Next, using Planck\u2019s relation E=hfE = hf, we calculate the <strong>energy<\/strong> carried by a single photon. Planck&#8217;s constant hh connects the wave (frequency) and particle (energy) nature of light. The resulting energy is 3.821\u00d710\u2212193.821 \\times 10^{-19} joules, a very small value, as expected for individual photons. However, when dealing with large numbers of photons (like in a laser beam), the cumulative energy becomes significant. To express this energy in a more practical unit for atomic and quantum processes, we convert joules to <strong>electron volts<\/strong>, yielding 2.38 eV.<\/p>\n\n\n\n<p>Finally, we compute the <strong>momentum<\/strong> using p=h\u03bbp = \\frac{h}{\\lambda}, which reflects that even massless particles like photons have momentum, critical in understanding phenomena like radiation pressure and the photoelectric effect.<\/p>\n\n\n\n<p>These calculations show how fundamental constants link the electromagnetic nature of light with quantum behavior, reinforcing the photon model of light.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-170.jpeg\" alt=\"\" class=\"wp-image-224326\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A photon of green light has a wavelength of 520 nm. Find the photon&#8217;s frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts The Correct Answer and Explanation is: To find the frequency, momentum, and energy of a green light photon with a wavelength of 520 nm, we\u2019ll use [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-224325","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224325","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224325"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224325\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}