6.1 Blackbody Radiation

Wien's displacement and Stefan's laws for thermal emission, and Planck's quantized oscillator energies resolving the ultraviolet catastrophe.

University Physics Volume 3, 6.1 Blackbody Radiation

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12 exercises

6.1 Exercise 1

The flame of a peach-scented candle has a yellowish color and the flame of a Bunsen’s burner in a chemistry lab has a bluish color. Which flame has a higher temperature?

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6.1 Exercise 2

An iron poker is being heated. As its temperature rises, the poker begins to glow—first dull red, then bright red, then orange, and then yellow. Use either the blackbody radiation curve or Wien’s law to explain these changes in the color of the glow.

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6.1 Exercise 3

Suppose that two stars, $\alpha$ and $\beta ,$ radiate exactly the same total power. If the radius of star $\alpha$ is three times that of star $\beta ,$ what is the ratio of the surface temperatures of these stars? Which one is hotter?

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6.1 Exercise 4

A molecule is vibrating at a frequency of $5.0 \times 10^{14} \text{Hz} .$ What is the smallest spacing between its vibrational energy levels?

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6.1 Exercise 5

Would the result in the example be different if the mass were not 1.0 kg but a tiny mass of 1.0 µg, and the amplitude of vibrations were 0.10 µm?

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6.1 Exercise 6

Which surface has a higher temperature – the surface of a yellow star or that of a red star?

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6.1 Exercise 8

Explain the color changes in a hot body as its temperature is increased.

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6.1 Exercise 10

Two cavity radiators are constructed with walls made of different metals. At the same temperature, how would their radiation spectra differ?

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6.1 Exercise 12

If everything radiates electromagnetic energy, why can we not see objects at room temperature in a dark room?

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6.1 Exercise 14

A 200-W heater emits a 1.5-µm radiation. (a) What value of the energy quantum does it emit? (b) Assuming that the specific heat of a 4.0-kg body is $0.83 \text{kcal} / \text{kg} \cdot \text{K} ,$ how many of these photons must be absorbed by the body to increase its temperature by 2 K? (c) How long does the heating process in (b) take, assuming that all radiation emitted by the heater gets absorbed by the body?

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6.1 Exercise 16

(a) For what temperature is the peak of blackbody radiation spectrum at 400 nm? (b) If the temperature of a blackbody is 800 K, at what wavelength does it radiate the most energy?

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6.1 Exercise 18

Interstellar space is filled with radiation of wavelength $970 \mu \text{m}.$ This radiation is considered to be a remnant of the “big bang.” What is the corresponding blackbody temperature of this radiation?

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