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3/10/2015 Black body radiation • A black body absorbs all incident light and converts the light's energy into thermal energy (no light is reflected). Modern Physics 2 Quantum Optics-ch26 • The black body then radiates electromagnetic waves based solely on its temperature. Physics 116 Eyres © 2014 Pearson Education, Inc. What characterizes a black body? • We can model a black body as the surface of a small hole in the side of a closed container. • The graph is called a spectral curve. Studies of black body radiation • If we raise the temperature of the box and again measure the spectrum of the EM radiation being emitted from the hole, we find that: • The total power output from the hole is now greater. • The spectral curve rises at all wavelengths. • The peak of the power per small wavelength interval shifts to a shorter wavelength. © 2014 Pearson Education, Inc. The color of stars © 2014 Pearson Education, Inc. • Very hot stars (around 10,000 K) look blue. • Even hotter stars are generally invisible to our eyes. Planck's hypothesis • Planck hypothesized that charged particles could radiate energy only in discrete portions called quanta. • He proposed that each microscopic oscillating charged particle had some kind of fundamental portion of energy, which was proportional to the frequency of its oscillation. • According to Planck, the particle could emit amounts of energy equal only to multiples of this fundamental portion. More Blue …… more Red © 2014 Pearson Education, Inc. © 2014 Pearson Education, Inc. 1 3/10/2015 Work function Photoelectric Effect • The work function is the minimum energy needed to remove a free electron from a metal. • The work function has units of energy but is measured in electron volts because it is typically very small. • The greater the work function of a metal, the more tightly the free electrons are bound to the metal and the more energy must be added to separate them. © 2014 Pearson Education, Inc. © 2014 Pearson Education, Inc. Photoelectric Effect Photoelectric Effect Freq (x 1014 Hz) KE (x 10-19 J) KE vs f photoelectric effect wavelength (nm) Volts (V) 2.11 0.94 6.32 1.50 G 1.87 0.73 G 5.61 1.17 Y 1.72 0.64 Y 5.17 1.02 O 1.67 0.52 O 5.00 0.83 R 1.43 0.34 R 4.29 0.54 UV max 2.30 1.52 UV max 6.90 2.43 UV min 2.73 1.52 UV min 8.20 2.43 Quantum model explanation of the photoelectric effect • According to Planck, the energy of a quantum of EM radiation is proportional to its frequency. • Using this idea, Einstein developed the following equation: K = (0.542 x10-33 Js)f - 1.7917 J 3.00 2.50 KE (x10^-19 J) B B Value of Plank’s constant is: 6.63 X 10-34 Js How do these results compare to theory? 2.00 1.50 1.00 0.50 0.00 0.00 2.00 4.00 6.00 8.00 10.00 freq (x10^14 Hz) Cutoff Frequency and Work Function We can express the cutoff frequency in terms of the work function of the metal and Planck's constant: If the energy of one quantum is less than the work function of the metal, and no photocurrent is produced. © 2014 Pearson Education, Inc. 2 3/10/2015 Checking Understanding Example 26.6 • Light and UV radiation shine on three different metals. Graph lines representing the stopping potential versus the incident light or UV frequency are shown below. The work functions of the metals are sodium (Na), 2.3 eV; iron (Fe), 4.7 eV; and platinum (Pt), 6.4 eV. Use Einstein's hypothesis of light absorption to explain the results. In the photoelectric effect experiment, why does red light not cause the emission of an electron though blue light can? A. The photons of red light don’t have sufficient energy to eject an electron. B. The electric field of the red light oscillates too slowly to eject an electron. C. Red light contains fewer photons than blue, not enough to eject electrons. D. The red light doesn’t penetrate far enough into the metal electrode. Threshold for Tissue Damage Checking Understanding In the photoelectric effect experiment, as we increase the frequency of the light what change do we see? A. There are more electrons emitted. B. The emitted electrons are faster. C. Both A and B. D. Neither A nor B. Wave-like and particle-like properties of photons Exposure to a sufficient quantity of ultraviolet will redden the skin, producing erythema—a sunburn. The amount of exposure necessary to produce this reddening depends on the wavelength. For a 1.0 cm2 patch of skin, 3.7 mJ of ultraviolet of 254 nm will produced reddening; at 300 nm, 13 mJ are required. A. What is the photon energy corresponding to each of these wavelengths? B. How many total photons do each of these exposures correspond to? C. Explain why there is a difference in the number of photons needed to provoke a response in the two cases. Photon momentum • Photons participate in collisions with electrons inside metals (the photoelectric effect). • This suggests that photons must have momentum. • In 1922, Arthur Compton performed a testing experiment to determine whether this expression was reasonable. © 2014 Pearson Education, Inc. © 2014 Pearson Education, Inc. 3 3/10/2015 The Compton effect and X-ray interference © 2014 Pearson Education, Inc. 4