{"id":4257,"date":"2024-09-22T16:17:08","date_gmt":"2024-09-22T16:17:08","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4257"},"modified":"2024-09-22T16:17:09","modified_gmt":"2024-09-22T16:17:09","slug":"the-seed-of-quantum-physics-plancks-formula","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/the-seed-of-quantum-physics-plancks-formula\/","title":{"rendered":"THE SEED OF QUANTUM PHYSICS: PLANCK\u2019S FORMULA"},"content":{"rendered":"\n

Returning to our story about the Ultraviolet Catastrophe, Einstein suggested solving it by using a mathematical \u201ctrick\u201d that had been proposed 5 years earlier by Max Planck when he was trying to improve upon the Wien approximation. Planck produced a formula that matched the data very well by assuming that the harmonic oscillators could not oscillate at any frequency, but instead were limited to a set of discrete, integer multiples of a fundamental unit of energy, E<\/em>, proportional to the oscillation frequency f<\/em>:\u2020<\/sup><\/a><\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

where h<\/em> = 6.626 \u00d7 10\u221234<\/sup> J \u00b7 s, is the constant that is now known as Planck\u2019s Constant.<\/em> Planck introduced this as a mathematical ploy to reduce the number of possible harmonic oscillators vibrating at high frequencies in the blackbody, thus reducing the average energy at those frequencies by application of the equipartition theorem. In this way Planck was able to come up with a formula where the radiated power decreases toward zero at high frequencies, yielding a finite total power that closely matches experimental data. Planck\u2019s Radiation Law predicts the intensity I<\/em> radiated by the blackbody at each wavelength \u03bb for any temperature T<\/em> according to:<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

where k<\/em> = 1.38 \u00d7 10\u221223<\/sup> J\/\u00b0K is Boltzmann\u2019s constant.<\/p>\n\n\n\n

Planck believed that this quantization<\/em> (allowing only discrete, integer multiples of frequency) applied only to the imaginary harmonic oscillators that were thought to exist in the walls of the blackbody cavity. Planck did not attribute any physical significance to this assumption, and believed that it was merely a mathematical device that enabled him to derive a single expression for the blackbody spectrum that matched the empirical data at all wavelengths.<\/p>\n\n\n\n

As we will see in chapter 4, we now know that Planck\u2019s assumed quantized oscillators are the very atoms that make the blackbody, and that these atoms radiate energy when electrons jump between a higher energy level to a lower energy level.<\/p>\n\n\n\n

Go back over this short section, and try to understand it really well! The simple expression E = hf<\/em> is at the very core of quantum physics! You will see this expression, as well as Planck\u2019s constant h<\/em> = 6.626 \u00d7 10\u221234<\/sup> J \u00b7 s very often in the sections and chapters that follow.<\/p>\n","protected":false},"excerpt":{"rendered":"

Returning to our story about the Ultraviolet Catastrophe, Einstein suggested solving it by using a mathematical \u201ctrick\u201d that had been proposed 5 years earlier by Max Planck when he was trying to improve upon the Wien approximation. Planck produced a formula that matched the data very well by assuming that the harmonic oscillators could not […]<\/p>\n","protected":false},"author":1,"featured_media":4171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[512],"tags":[],"class_list":["post-4257","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-light-as-particles"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/bulb.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4257","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4257"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4257\/revisions"}],"predecessor-version":[{"id":4261,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4257\/revisions\/4261"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4171"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}