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p1041.pdf - The Dawn of the Quantum Theory As suggested we...

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Unformatted text preview: The Dawn of the Quantum Theory As suggested, we let x = he/(AmxkB T), and then d d 87rhc 1 :17 [Raj] = Z): < k5 ehc/AkBT __ l) -5 8‘ 1 O = 817;": .3...— " "ST—(1227 Am“ (e‘ — 1) Am“ (eJr —— 1) xe‘ 25(3‘ — 1) To solve, we iterate and find x = hc/AmukBT = 4.965, or AmuT = 2.90 x 10”3 m-K. . t what wavelength does the maximum in the radiant energy density distribution function for a c ackbody occur if (a) T = 300 K? (b) T = 3000 K? (c) T =‘ 10000 K? From Equation 1.4, __ 2.90 ><10‘3 m-K a. A. ___ . —6 max 300 K 9 67 x 10 m 2.90 x 10*3 m-K b. A = _____—— = 9 7 ‘7 max 3 K .6 x 10 m 2.90 x 10—3 m~K c. A = ___—————— = 2.90 10'7 W IOOOOK X m 1—7. Sirius, one of the hottest known stars, has approximately a blackbody spectrum with Am“ 2 260 nm. Estimate the surface temperature of Sirius. From Equation 1.4, 2.90 x 10‘3 m-K 2.90 x 10-3 m'K T::———————=————-——-———=1.12 104K A 260x 10‘9m X max 1—8. e fireball in a thermonuclear explosion can reach temperatures of approximately 107 K. What v . ue of Arm does this correspond to? In what region of the spectrum is this wavelength found (cf. Figure 1.11)? From Equation 1.4, 2.9Ox10'3m-K A =———.—————= "0 mu 1x107K 3x10 m This corresponds to the X—ray region in the electromagnetic spectrum. 1—9. Calculate the energy of a photon for a wavelength of 100 pm (about one atomic diameter). ...
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