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

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?

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

Cosmic Microwave Background Radiation

The Cosmic Microwave Background (CMB) is the remnant thermal radiation from the early stages of the universe, often modeled as a nearly perfect blackbody. Studying the CMB provides insight into the early universe's conditions, supporting evidence for the Big Bang theory and offering a way to determine cosmological parameters such as temperature at different epochs.

Recombination and Universe Transparency

Recombination refers to the epoch in the early universe when electrons combined with protons to form neutral hydrogen, allowing photons to decouple from matter and travel freely through space. This marked the time when the universe became transparent, leaving behind the cosmic microwave background. Understanding this process is crucial for studying the evolution of the universe and interpreting observational data from the CMB.

Wien's Law

Wien's Law relates the temperature of a blackbody to the wavelength at which it emits radiation most intensely, through the formula ?_max * T = constant. This fundamental principle in thermal radiation provides a practical means to determine the temperature of objects by observing their peak emission wavelength, and it plays a critical role in understanding the thermal properties of various astronomical phenomena.

Blackbody Radiation

Blackbody radiation describes the emission of electromagnetic radiation by an idealized object that absorbs all incident light. The emission spectrum of a blackbody is solely determined by its temperature, leading to a characteristic distribution of wavelengths. This concept underpins much of modern astrophysics, allowing scientists to analyze and infer temperatures and compositions of stars and cosmic background radiation.

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