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Unformatted text preview: Solutions to Homework #11 Chapter 30 8. Picture the Problem : An incandescent light bulb operates at a cooler temperature than a halogen bulb. Therefore, the blackbody radiation from the two light bulbs will have different peak frequencies. Strategy: According to Wiens Displacement Law, a hotter bulb will emit light with a higher peak frequency. Because the halogen bulb is hotter, it will emit a higher peak frequency than the incandescent bulb. Use Wiens Displacement Law (equation 30-1) to calculate both of the peak frequencies and calculate their ratio. Solution: 1. (a) Because peak , f T the halogen bulb has the higher peak frequency. 2. (b) Calculate the ratio of the peak frequencies: ( 29 ( 29 10 1 1 hal hal 10 1 1 std std 5.88 10 s K 3400 K 1.2 2900 K 5.88 10 s K T f f T---- = = = 3. (c) Calculate the peak frequencies of the two bulbs: ( 29 ( 29 ( 29 ( 29 10 1 1 14 hal 10 1 1 14 std 5.88 10 s K 3400 K 2.0 10 Hz 5.88 10 s K 2900 K 1.7 10 Hz f f---- = = = = 4. The halogen bulb produces a peak frequency that is closer to 14 5.5 10 Hz than the standard incandescent bulb. Insight: Because the halogen bulb produces a peak frequency closer to the sensitive frequencies of the human eye, more of the radiation from the halogen bulb is visible, making it appear brighter for the same power output. 12. Picture the Problem : A source of red light has a higher wattage than a source of green light. Strategy: Use the expression for photon energy (equation 30-4) to answer the conceptual question. Solution: 1. (a) The energy of photons emitted by the red source is less than the energy of photons emitted by the green source, regardless of the wattage of the source. This conclusion follows from the relation E = h f and the fact that green light has a higher frequency than red light. 2. (b) The best explanation is II . The red-source photons have less energy than the green-source photons because they have a lower frequency. The wattage of the source doesnt matter. Statements I and III are each false. Insight: A higher wattage source in general produces more photons than does a lower wattage source, but the energy of each photon is determined by the frequency, not the power of the source. 26. Picture the Problem : The light from the laser can be considered as the emission of many photons of the same wavelength. The power output is the product of the photon emission rate and the energy of each photon....
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