{"id":194461,"date":"2025-02-24T06:27:43","date_gmt":"2025-02-24T06:27:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194461"},"modified":"2025-02-24T06:27:46","modified_gmt":"2025-02-24T06:27:46","slug":"the-first-ionization-energy-of-a-hydrogen-atom-is-1-31-kj-mol","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/24\/the-first-ionization-energy-of-a-hydrogen-atom-is-1-31-kj-mol\/","title":{"rendered":"The first ionization energy of a hydrogen atom is 1.31 kJ\/mol"},"content":{"rendered":"\n<p>The first ionization energy of a hydrogen atom is 1.31 kJ\/mol. What is the wavelength of light, in nanometers, that is just sufficient to ionize a hydrogen atom? Refer to the values for constants.<\/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 determine the wavelength of light that is just sufficient to ionize a hydrogen atom, we use the relationship between energy and wavelength given by the equation:<\/p>\n\n\n\n<p>[<br>E = \\frac{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 required to ionize a hydrogen atom (first ionization energy),<\/li>\n\n\n\n<li>(h) is Planck\u2019s constant ((6.626 \\times 10^{-34} \\, \\text{J\u00b7s})),<\/li>\n\n\n\n<li>(c) is the speed of light ((3.00 \\times 10^8 \\, \\text{m\/s})),<\/li>\n\n\n\n<li>(\\lambda) is the wavelength in meters.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert Energy to Joules<\/h3>\n\n\n\n<p>The given ionization energy is:<\/p>\n\n\n\n<p>[<br>1.31 \\times 10^3 \\, \\text{kJ\/mol} = 1.31 \\times 10^6 \\, \\text{J\/mol}<br>]<\/p>\n\n\n\n<p>Since this energy is per mole, we convert it to energy per atom using Avogadro\u2019s number ((6.022 \\times 10^{23}) atoms\/mol):<\/p>\n\n\n\n<p>[<br>E = \\frac{1.31 \\times 10^6 \\text{ J\/mol}}{6.022 \\times 10^{23} \\text{ atoms\/mol}}<br>]<\/p>\n\n\n\n<p>[<br>E = 2.176 \\times 10^{-18} \\text{ J\/atom}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for Wavelength<\/h3>\n\n\n\n<p>Using (E = \\frac{hc}{\\lambda}), we rearrange for (\\lambda):<\/p>\n\n\n\n<p>[<br>\\lambda = \\frac{hc}{E}<br>]<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>[<br>\\lambda = \\frac{(6.626 \\times 10^{-34} \\text{ J\u00b7s}) (3.00 \\times 10^8 \\text{ m\/s})}{2.176 \\times 10^{-18} \\text{ J}}<br>]<\/p>\n\n\n\n<p>[<br>\\lambda = 9.11 \\times 10^{-8} \\text{ m}<br>]<\/p>\n\n\n\n<p>Converting meters to nanometers:<\/p>\n\n\n\n<p>[<br>\\lambda = 91.1 \\text{ nm}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The wavelength of light required to ionize a hydrogen atom is <strong>91.1 nm<\/strong>.<\/p>\n\n\n\n<p>This wavelength falls in the <strong>ultraviolet (UV) region<\/strong>, meaning hydrogen atoms require UV light for ionization.<\/p>\n\n\n\n<p>Now, I will generate an image representing the hydrogen ionization process.<\/p>\n\n\n\n<p>The image visually represents the ionization of a hydrogen atom, showing an ultraviolet (UV) photon striking the atom and ejecting its electron. This process illustrates how light with a wavelength of 91.1 nm provides sufficient energy to ionize the atom. Let me know if you need any modifications!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1335.png\" alt=\"\" class=\"wp-image-194462\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The first ionization energy of a hydrogen atom is 1.31 kJ\/mol. What is the wavelength of light, in nanometers, that is just sufficient to ionize a hydrogen atom? Refer to the values for constants. The Correct Answer and Explanation is : To determine the wavelength of light that is just sufficient to ionize a hydrogen [&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-194461","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194461","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=194461"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194461\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}