{"id":186816,"date":"2025-01-26T09:12:00","date_gmt":"2025-01-26T09:12:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186816"},"modified":"2025-01-26T09:12:03","modified_gmt":"2025-01-26T09:12:03","slug":"a-photon-of-red-light-wavelength-690-nm-and-a-ping-pong-ball-mass-2-60-a1-10-3-kg","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/26\/a-photon-of-red-light-wavelength-690-nm-and-a-ping-pong-ball-mass-2-60-a1-10-3-kg\/","title":{"rendered":"A photon of red light (wavelength = 690 nm) and a Ping-Pong ball (mass = 2.60 A1 10-3\u00a0kg)"},"content":{"rendered":"\n<p>A photon of red light (wavelength = 690 nm) and a Ping-Pong ball (mass = 2.60 A1 10<sup>-3<\/sup>\u00a0kg) have the same momentum. At what speed is the ball moving?<\/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 find the speed of the Ping-Pong ball, we will first calculate the momentum of the photon and equate it to the momentum of the Ping-Pong ball. The formula for momentum ( p ) is:<\/p>\n\n\n\n<p>[<br>p = mv<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( m ) is the mass of the object (for the ball),<\/li>\n\n\n\n<li>( v ) is its velocity (which we want to solve for).<\/li>\n<\/ul>\n\n\n\n<p>The momentum of a photon is given by the relation:<\/p>\n\n\n\n<p>[<br>p = \\frac{h}{\\lambda}<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( h ) is Planck&#8217;s constant (( 6.626 \\times 10^{-34} \\, \\text{J\u00b7s} )),<\/li>\n\n\n\n<li>( \\lambda ) is the wavelength of the light.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the momentum of the photon<\/h3>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Wavelength ( \\lambda = 690 \\, \\text{nm} = 690 \\times 10^{-9} \\, \\text{m} )<\/li>\n<\/ul>\n\n\n\n<p>We use the formula for the photon&#8217;s momentum:<\/p>\n\n\n\n<p>[<br>p_{\\text{photon}} = \\frac{h}{\\lambda}<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>p_{\\text{photon}} = \\frac{6.626 \\times 10^{-34}}{690 \\times 10^{-9}} \\approx 9.61 \\times 10^{-28} \\, \\text{kg\u00b7m\/s}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Equate the momentum of the ball to the momentum of the photon<\/h3>\n\n\n\n<p>Since the photon and the Ping-Pong ball have the same momentum:<\/p>\n\n\n\n<p>[<br>p_{\\text{ball}} = p_{\\text{photon}}<br>]<\/p>\n\n\n\n<p>[<br>m_{\\text{ball}} v = p_{\\text{photon}}<br>]<\/p>\n\n\n\n<p>We can solve for the speed of the ball ( v ):<\/p>\n\n\n\n<p>[<br>v = \\frac{p_{\\text{photon}}}{m_{\\text{ball}}}<br>]<\/p>\n\n\n\n<p>Substitute the given mass of the Ping-Pong ball (( m_{\\text{ball}} = 2.60 \\times 10^{-3} \\, \\text{kg} )):<\/p>\n\n\n\n<p>[<br>v = \\frac{9.61 \\times 10^{-28}}{2.60 \\times 10^{-3}} \\approx 3.69 \\times 10^{-25} \\, \\text{m\/s}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The speed of the Ping-Pong ball is approximately ( 3.69 \\times 10^{-25} \\, \\text{m\/s} ). This is an extremely small velocity, as the ball has much more mass than the photon, making it much slower than light in terms of speed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A photon of red light (wavelength = 690 nm) and a Ping-Pong ball (mass = 2.60 A1 10-3\u00a0kg) have the same momentum. At what speed is the ball moving? The Correct Answer and Explanation is : To find the speed of the Ping-Pong ball, we will first calculate the momentum of the photon and equate [&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-186816","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186816","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=186816"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186816\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}