Black Body Radiation and Planck's Quantum Hypothesis
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1 Section 3: Black Body Radiation and Planck's Quantum Hypothesis Definitions Opaque materials: materials in which no light is allowed to pass through; all light is either absorbed or reflected. Radiation: Energy travelling in the form of electromagnetic waves or photons. 1
2 A. What is a blackbody and what is blackbody radiation? Any opaque body that has a temperature above absolute zero (0 K = 273 ) radiates photons. We can feel the warmth of a fireplace, a stove element or sun without touching them. A blackbody is an ideal concept. It is that perfect object which absorbs all radiation that falls on it. Such a body is obviously "black" in the usual sense because it absorbs all light that falls on it. However, it also absorbs all other types of electromagnetic radiation that happens to strike it. Objects that are excellent absorbers are also excellent emitters. So, a blackbody (or an object that is very nearly like an ideal blackbody) will emit radiation more efficiently than any other object. This radiation is called blackbody radiation. 2
3 B. What's the best way to make a blackbody radiate energy? Heat it up! Consider the element on an electric range. As you turn up the current, the element first turns pink and then a deeper red. It is obviously emitting red light. But before it began to glow, it was emitting infrared radiation which we experience as heat. Of course, it continues to give off infrared along with the visible red light as it becomes hotter. In other words, the element is emitting a range of wavelengths (or, if you like, a range of frequencies). You have probably seen industrial films or videos where objects become so hot that they pass through the red phase and emit orangered, then yellow, and, if made hot enough, white light which is really a mixture of all the rainbow colours. Much of the radiation, however, is still in the infrared range. Our eyes are very good detectors for the frequencies from red to blue, but we cannot see infrared. However, if you hold your hand close to a hot body you can feel the heating effects of infrared radiation. 3
4 Imagine that the intensity of radiation is measured as it is emitted from a red hot electric stove element. A characteristic graph is shown below. It takes a little effort to get use to the graph. Here are some things that you should note: the graph is not showing a change in temperature. The temperature of the element is fixed and therefore is the same everywhere on the curve. the x axis is not time. That is, the graph is not saying that at first the element was red and then started to emit heat. the graph is a snap shot of the type of radiation from the element. There is definitely some red light, but you can tell from the bump that the maximum radiated intensity has a wavelength that is beyond the red and well into the infrared region. 4
5 A Family of Graphs of the Emitted Radiation for Three Different Temperatures There are two things that you should notice about the set of three graphs above: the intensity of radiation increases as the temperature of the blackbody increases. This should come as no surprise. as temperature increases the peaks shift to the left. Note that the peak of graph 2 occurs at a smaller wavelength (and larger frequency) that does the peak of graph 1. And the peak intensity of graph 3 has a wavelength than is smaller that that of graph 2. You should be able to see that for the extremely hot blackbody (graph 3) some of the radiation is actually in the ultraviolet frequency range, and the peak energy emission has a wavelength that is very close to that of visible red. 5
6 1 What is the energy of a photon whose wavelength is 510 nm? a) 2.4 ev b) 3.9 ev c) 6.2 ev d) 0.4 ev 2 Which statement is false? a) hot tea will cool faster in a black teapot than in a white teapot b) ice cream will melt faster in a black tub than in white tub c) A black ball and a white ball that have been sitting in the same room for days will have the same temperature d) A black object absorbs radiation very well, but is a poor emitter of radiation. 3 According to the 4 emission graphs shown, which hot object will we see glowing the reddest? a) 1 b) 2 c) 3 d) 4 4 According to the 4 emission graphs of #2, for which object would our eyes be no good in helping us to determine if the object was hot? a) 1 b) 2 c) 3 d) 4 6
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