{"id":41843,"date":"2025-06-28T11:24:54","date_gmt":"2025-06-28T11:24:54","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=41843"},"modified":"2025-06-28T11:25:03","modified_gmt":"2025-06-28T11:25:03","slug":"a-photon-of-red-light-wavelength-680-nm-and-a-ping-pong-ball-mass-1-90-x-10-3-kg-have-the-same-momentum","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-photon-of-red-light-wavelength-680-nm-and-a-ping-pong-ball-mass-1-90-x-10-3-kg-have-the-same-momentum\/","title":{"rendered":"A photon of red light (wavelength = 680 nm) and a Ping-Pong ball (mass = 1.90 \u00d7 10-3 kg) have the same momentum"},"content":{"rendered":"\n<p>A photon of red light (wavelength = 680 nm) and a Ping-Pong ball (mass = 1.90 \u00d7 10-3 kg) have the same momentum. At what speed is the ball moving?<\/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 find the speed of the Ping-Pong ball, we use the fact that both the photon and the ball have the same momentum. The momentum of a photon is given by: p=h\u03bbp = \\frac{h}{\\lambda}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>pp is momentum<\/li>\n\n\n\n<li>h=6.626\u00d710\u221234\u2009J\\cdotpsh = 6.626 \\times 10^{-34} \\, \\text{J\u00b7s} (Planck&#8217;s constant)<\/li>\n\n\n\n<li>\u03bb=680\u2009nm=680\u00d710\u22129\u2009m\\lambda = 680 \\, \\text{nm} = 680 \\times 10^{-9} \\, \\text{m}<\/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>p=6.626\u00d710\u221234680\u00d710\u22129=9.74\u00d710\u221228\u2009kg\\cdotpm\/sp = \\frac{6.626 \\times 10^{-34}}{680 \\times 10^{-9}} = 9.74 \\times 10^{-28} \\, \\text{kg\u00b7m\/s}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use this momentum to find the speed of the Ping-Pong ball<\/h3>\n\n\n\n<p>Momentum is also defined for classical objects as: p=mvp = mv<\/p>\n\n\n\n<p>Solving for velocity vv: v=pm=9.74\u00d710\u2212281.90\u00d710\u22123=5.13\u00d710\u221225\u2009m\/sv = \\frac{p}{m} = \\frac{9.74 \\times 10^{-28}}{1.90 \\times 10^{-3}} = 5.13 \\times 10^{-25} \\, \\text{m\/s}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>5.13\u00d710\u221225\u2009m\/s\\boxed{5.13 \\times 10^{-25} \\, \\text{m\/s}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>To compare the motion of a photon and a Ping-Pong ball, we must use the concept of momentum. A photon, which has no mass, still carries momentum. Its momentum is calculated using Planck&#8217;s constant and its wavelength. In this case, the red light photon has a wavelength of 680 nanometers, which we convert to meters to keep all units consistent in the SI system.<\/p>\n\n\n\n<p>By dividing Planck&#8217;s constant by the wavelength, we find the photon\u2019s momentum to be approximately 9.74\u00d710\u221228\u2009kg\\cdotpm\/s9.74 \\times 10^{-28} \\, \\text{kg\u00b7m\/s}. Since the problem states that the Ping-Pong ball has the same momentum as the photon, we set the two momenta equal.<\/p>\n\n\n\n<p>To find the ball\u2019s speed, we apply the classical formula for momentum, which is mass times velocity. Rearranging the formula to solve for velocity, we divide the momentum by the ball&#8217;s mass. The Ping-Pong ball has a mass of 1.90\u00d710\u22123\u2009kg1.90 \\times 10^{-3} \\, \\text{kg}, so its velocity becomes incredibly small, about 5.13\u00d710\u221225\u2009m\/s5.13 \\times 10^{-25} \\, \\text{m\/s}.<\/p>\n\n\n\n<p>This extremely low speed shows how large and massive objects must move very slowly to match the tiny momentum of a single photon. The result also emphasizes how different quantum objects like photons are from macroscopic objects like a ball. Despite having the same momentum, the scale of motion between them differs greatly due to the massive difference in mass.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A photon of red light (wavelength = 680 nm) and a Ping-Pong ball (mass = 1.90 \u00d7 10-3 kg) 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 use the fact that both the photon and the ball [&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-41843","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41843","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=41843"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41843\/revisions"}],"predecessor-version":[{"id":41844,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41843\/revisions\/41844"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=41843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=41843"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=41843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}