The ultraviolet catastrophe and Planck's quantum hypothesis
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5 quick questions — pick an answer to see if you’re right.
1. An element absorbs light at certain colors. Compared to the colors it emits, they are…
2. How many different spectral lines can an atom with 4 energy levels produce?
3. Each element gives off a unique pattern of colors called a…
4. How do astronomers know what distant stars are made of?
5. Which statement about atoms is supported by blackbody results?
Stars behave approximately like blackbodies: the wavelength at which they glow most brightly depends on their surface temperature. The red supergiant Betelgeuse has a surface temperature of about 3500 K, the Sun about 5800 K, and the blue-white star Rigel about 12,000 K.
Which star’s radiation peaks at the shortest wavelength?
Challenge score: 0 / 6
C1. An electric stove burner heats up. In what order does it change color?
C2. The wavelength of peak emission is given by Wien’s law, λmax = 2.90 × 10−3 m·KT. Substitute numerical values into this mathematical representation to determine the peak wavelength for Betelgeuse. Then calculate it.
C3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship. (Wien’s law, λmax = 2.90 × 10−3 m·KT)
C4. A thermal camera detects a person whose skin temperature is about 310 K. Using Wien’s law, λmax = 2.90 × 10−3 m·KT, determine the person’s peak wavelength in micrometers (1 µm = 10−6 m).
C5. Classical physics predicted that a blackbody should emit enormous amounts of ultraviolet radiation, which does not happen. How did Max Planck fix this?
C6. An incandescent bulb filament glows at about 2800 K, so most of its radiation is infrared. An engineer proposes running the filament at a higher temperature. Identify one benefit and one drawback of this design change.