Quantum Theory: Understanding Light and Matter Waves, Exams of Business Management and Analysis

Download Quantum Theory: Understanding Light and Matter Waves and more Exams Business Management and Analysis in PDF only on Docsity! 1 Quantum Theory (cont) Announcements 1) Exam 2 will be returned by next Friday Quantum Theory Continued Classical Picture Quantum Picture Energy of wave ∝ (Amplitude)2 Energy/photon = hc / λ 2 Photoelectric Effect demo - + Electrons flow !! - + More electrons flow !! Recall Ephoton = hc/λ. Since (λred~ 700 nm) > (λblue~ 450 nm) è red photons are less energetic than blue ones ! è Blue light knocks out more electrons è larger current ! Example from book P 358: On a clear day, the sunlight striking each square meter of Earth’s surface corresponds to 1000 [J] per second. Estimate the number of photons striking 1 square meter during that second. Assume sunlight is mostly in the visible region. According to quantum theory Energy/photon is: E = hc / λ = (6.6x10-34)(3x108) / 5x10-7 = 4x10-19 [J] Visible photon wavelength is about 500 [nm] = 5x10-7 [m] Number of these photons in 1000 [J] is: # photons = Total energy / (Energy/photon) = 1000 [J] / 4x10-19 [J/photon] = 2.5x1021 photons That’s a lot of photons !!! 1 m 1 m 5 Real photographs of an electron interference pattern… .01 [s] 10 electrons .1 [s] 100 electrons 3 [s] 3000 electrons 20 [s] 20,000 electrons 70 [s] 70,000 electrons Notice the clear interference fringes. Clear indication of wave phenomenon. Matter Waves (example) Compute the wavelength of a 0.001 [kg] bullet moving at 1000 [m/s]. (Since v is much less than c (3x108 m/s), ignore relativistic effects) λ = h/mv = 6.6x10-34 [J s] / (0.001 [kg])(1000 [m/s]) = 6.6x10-34 [m]. This is immeasureably small è For ordinary “everyday objects”, we don’t experience that matter can behave as a wave. 6 But, what about small particles ? Compute the wavelength of an electron (m = 9.1x10-31 [kg]) moving at 1x107 [m/s]. (v/c = 1x107/3x108 = 0.033 (small compared to 1) è ignore relativistic effects) λ = h/mv = 6.6x10-34 [J s]/(9.1x10-31 [kg])(1x107 [m/s]) = 7.3x10-11 [m]. = 0.073 [nm] These electrons have a wavelength in the region of X-rays How do we see ? Light reflects (scatters) from a surface and reaches our eye. Our eye forms an image of the object. 7 Wavelength versus Size Even with a visible light microscope, we are limited to being able to resolve objects which are at least about 10-6 [m] = 1 [µm] = 500 [nm] in size. This is because visible light, with a wavelength of ~500 [nm] cannot resolve objects whose size is smaller than it’s wavelength. Bacteria, as viewed using visible light Bacteria, as viewed using electrons (electron waves) ! Electron Microscope These images were taken with a Scanning Electron Microscope (SEM). These devices can resolve features down to about 1 [nm]. This is about 100 times better than can be done with visible light microscopes! èThe electron microscope is a device which uses the wave behavior of electrons to make images which are otherwise too small for visible light! IMPORTANT POINT HERE: High energy particles can be used to reveal what things look like (ie., their structure)