Recall that Planck introduced <\/strong>h<\/em> to describe the possible energies of a radiation oscillator in a cavity wall. The result was \u03b5 = <\/strong>nhf<\/em> where <\/strong>n = <\/em>0, 1, 2, \u2026 and <\/strong>f<\/em> is the frequency of the oscillator. <\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n

<\/strong> <\/p>\n

a) What are the dimensions of <\/strong>h<\/em>? <\/strong><\/strong><\/span><\/p>\n

b) It is reasonable to expect electrons in an atom are bound due to an electrostatic force <\/strong>ke<\/em>2<\/strong>\/<\/strong>r<\/em>2<\/strong>.<\/em> Consider a Hydrogen atom. Assuming the size of the electron orbit can only depend on the electronic charge <\/strong>e<\/em>, the electron mass <\/strong>m,<\/em>and Planck\u2019s constant <\/strong>h, <\/em>use dimensional analysis to determine how the size of the orbit <\/strong>r<\/em> must depend on <\/strong>e, m, <\/em>and <\/strong>h. <\/em>Use your result to estimate the size of an H atom. Is the size of such an orbit unambiguously determined by classical considerations? <\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/p>\n

c) Show that the \u201cfine structure constant\u201d \u03b1 \u2261 2\u03c0<\/strong>ke<\/em>2<\/strong>\/<\/strong>hc<\/em> is dimensionless and evaluate its value. <\/strong><\/strong><\/strong><\/span><\/p>\n

d) It is speculated that quantum mechanical effects are important for the gravitational interaction at a distance scale called the <\/strong>Planck length<\/em>. Using dimensional considerations determine how the Planck length depends on <\/strong>G, h,<\/em> and <\/strong>c. <\/em>Evaluate its value. <\/strong><\/strong><\/strong><\/strong><\/span><\/p>\n

2. Assume the energy of a photon of frequency <\/strong>f <\/em>to be given by \u03b5 = <\/strong>hf. <\/em>Consider light produced by a 50W monochromatic Sodium light source of wavelength \u03bb = 590nm. <\/strong><\/strong><\/strong><\/span><\/p>\n

a) <\/strong>Determine the energy of each photon in the Na light<\/strong><\/p>\n

b) <\/strong>At a distance of 40cm from the light source what is the density of photons per unit volume<\/strong>?<\/span><\/p>\n

c) <\/strong>What is the rate at which photons enter an eye pupil of area <\/strong>A =<\/em> 2mm<\/strong>2<\/strong> for the location of part (b)? <\/strong><\/strong><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

Recall that Planck introduced h to describe the possible energies of a radiation oscillator in a cavity wall. The result was \u03b5 = nhf where n = 0, 1, 2, \u2026 and f is the frequency of the oscillator. a) What are the dimensions of h? b) It is reasonable to expect electrons in an […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/153107"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=153107"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/153107\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=153107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=153107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=153107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}