The universe is filled with thermal radiation, which has a...

The universe is filled with thermal radiation, which has a blackbody spectrum at an effective temperature of $2.7 \mathrm{~K}$ (see Chapter 15 ). What is the peak wavelength of this radiation? What is the energy (in eV) of quanta at the peak wavelength? In what region of the electromagnetic spectrum is this peak wavelength?

Key Concepts

Cosmic Microwave Background Radiation

Cosmic Microwave Background (CMB) radiation is the remnant thermal radiation from the Big Bang, now observed as a nearly uniform blackbody spectrum at an effective temperature of about 2.7 K. It serves as a crucial observational pillar in cosmology, providing insights into the early universe and its subsequent evolution.

Photon Energy-Wavelength Relationship

The relationship between a photon's energy and its wavelength is given by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This concept allows the conversion of the peak wavelength of a thermal spectrum into the corresponding energy, which is especially useful when expressing photon energy in electron-volts (eV).

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, classified by their wavelengths or frequencies. The identification of the region in which a particular wavelength falls—such as the microwave, infrared, visible, ultraviolet, X-ray, or gamma-ray region—is fundamental in understanding the different behaviors and applications of electromagnetic waves.

Blackbody Radiation

Blackbody radiation refers to the theoretical spectrum of electromagnetic radiation emitted by an object that absorbs all incident radiation and is in thermal equilibrium. This concept underpins the study of thermal emission from bodies and is foundational in understanding how objects emit radiation based on their temperature, following Planck's law.

Wien's Displacement Law

Wien's displacement law is the principle that establishes the relationship between the temperature of a blackbody and the wavelength at which it emits radiation most intensely. It shows that the peak wavelength is inversely proportional to the temperature, allowing one to determine the peak wavelength of the emission given a specific temperature.

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