35. Special Relativity
Consequences of Relativity
11:11 minutes
Problem 36.65
Textbook Question
Textbook Question(III) A certain atom emits light of frequency ƒ₀ when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward, and others away from, an observer due to their random thermal motion. Using the rms speed of thermal motion, (a) show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is ∆ƒ/ƒ₀ ≈ 2 √3kT/mc². Assume mc² ≫ 3kT. (b) Evaluate ∆ƒ/ƒ₀ for a gas of hydrogen atoms at 650 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
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