Cosmology Use Wien's law (see Problem 37) to answer the...

Cosmology Use Wien's law (see Problem 37) to answer the following questions: (a) The cosmic background radiation peaks in intensity at a wavelength of 1.1 $\mathrm{mm}$ . To what temperature does this correspond? (b) About 379000 $\mathrm{y}$ after the big bang, the universe became transparent to electromagnetic radiation. Its temperature then was 2970 $\mathrm{K} .$ What was the wavelength at which the background radiation was then most intense?

Cosmology
Use Wien's law (see Problem 37) to answer the following questions: (a) The cosmic background radiation peaks in intensity at a wavelength of 1.1 $\mathrm{mm}$ . To what temperature does this correspond? (b) About 379000 $\mathrm{y}$ after the big bang, the universe became transparent to electromagnetic radiation. Its temperature then was 2970 $\mathrm{K} .$ What was the wavelength at which the background radiation was then most intense?

Key Concepts

Recombination Epoch

The recombination epoch marks the time in the universe's history when it cooled sufficiently for protons and electrons to combine and form neutral hydrogen atoms. This reduction in free electrons allowed photons to travel freely, leading to the decoupling of matter and radiation and resulting in the cosmic microwave background radiation observed today.

Cosmic Microwave Background Radiation

The cosmic microwave background (CMB) radiation is the relic thermal radiation from the early universe, specifically from the epoch when the universe transitioned from being opaque to transparent. It is observed as a nearly uniform background of radiation and is a key piece of evidence supporting the Big Bang theory.

Blackbody Radiation

Blackbody radiation refers to the theoretical spectrum of electromagnetic radiation emitted by an idealized body that absorbs all incident radiation, irrespective of wavelength. The shape of the spectrum is solely determined by the temperature of the body, making blackbody radiation a central concept in understanding thermal emission processes in various physical contexts.

Wien's Displacement Law

Wien's displacement law is a principle in thermal radiation which states that the wavelength at which the emission of a blackbody spectrum is maximized is inversely proportional to its absolute temperature. This law is essential in determining the temperature of an object from the peak wavelength of its emitted radiation, and vice versa.

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