Quantum Physics

27.1 Blackbody Radiation and Planck’s Hypothesis 875continuous distribution of wavelengths from the infrared, visible, and ultravioletportions of the spectrum.From a classical viewpoint, thermal radiation originates from acceleratedcharged particles near the surface of an object; such charges emit radiation, muchas small antennas do. The thermally agitated charges can have a distribution of frequencies,which accounts for the continuous spectrum of radiation emitted by theobject. By the end of the 19th century, it had become apparent that the classicaltheory of thermal radiation was inadequate. The basic problem was in understandingthe observed distribution energy as a function of wavelength in the radiationemitted by a blackbody. By definition, a blackbody is an ideal system that absorbsall radiation incident on it. A good approximation of a blackbody is a small holeleading to the inside of a hollow object, as shown in Figure 27.1. The nature ofthe radiation emitted through the small hole leading to the cavity depends only onthe temperature of the cavity walls, and not at all on the material composition of theobject, its shape, or other factors.Experimental data for the distribution of energy in blackbody radiation at threetemperatures are shown in Active Figure 27.2 (page 876). The radiated energyvaries with wavelength and temperature. As the temperature of the blackbody increases,the total amount of energy (area under the curve) it emits increases. Also,with increasing temperature, the peak of the distribution shifts to shorter wavelengths.This shift obeys the following relationship, called Wien’s displacement law, max T 0.2898 10 2 m K [27.1]where max is the wavelength at which the curve peaks and T is the absolute temperatureof the object emitting the radiation.Figure 27.1 An opening in the cavityof a body is a good approximationof a blackbody. As light enters thecavity through the small opening, partis reflected and part is absorbed oneach reflection from the interior walls.After many reflections, essentially allof the incident energy is absorbed.TIP 27.1 Expect to BeConfusedYour life experiences take place inthe macroscopic world, where quantumeffects are not evident. Quantumeffects can be even more bizarre thanrelativistic effects, but don’t despair:confusion is normal and expected. Asthe Nobel prize-winning physicistRichard Feynman once said, “Nobodyunderstands quantum mechanics.”Applying Physics 27.1Star ColorsIf you look carefully at stars in the night sky, you candistinguish three main colors: red, white, and blue.What causes these particular colors?Explanation These colors result from the differentsurface temperatures of stars. A relatively cool star, witha surface temperature of 3 000 K, has a radiation curvelike the middle curve in Active Figure 27.2 (page 876).The peak in this curve is above the visible wavelengths,0.4 m–0.7m, beyond the wavelength of red light, sosignificantly more radiation is emitted within the visiblerange at the red end than the blue end of the spectrum.Consequently, the star appears reddish in color, similarto the red glow from the burner of an electric stove.A hotter star has a radiation curve more like the upper curve in Active Figure 27.2.In this case, the star emits significant radiation throughout the visible range, andthe combination of all colors causes the star to look white. This is the case with ourown Sun, with a surface temperature of 5 800 K. For very hot stars, the peak canbe shifted so far below the visible range that significantly more blue radiation isemitted than red, so the star appears bluish in color.EXAMPLE 27.1 Thermal Radiation from the Human BodyGoal Apply Wien’s law.Problem The temperature of the skin is approximately 35.0°C. At what wavelength does the radiation emitted fromthe skin reach its peak?Strategy This is a matter of substitution into Wien’s law, Equation 27.1.SolutionApply Wien’s displacement law: max T 0.289 8 10 2 m K