The COBE satellite was launched in 1989 to study the cosmic...

The COBE satellite was launched in 1989 to study the cosmic background radiation and measure its temperature. By measuring at many different wavelengths, researchers were able to show that the background radiation exactly followed the spectral distribution expected for a blackbody. At a wavelength of $0.133 \mathrm{cm},$ the radiant intensity is $1.440 \times 10^{-7} \mathrm{W} / \mathrm{m}^{2}$ in a wavelength interval of $0.00833 \mathrm{cm} .$ What is the temperature of the radiation that would be deduced from these data?

Key Concepts

Cosmic Microwave Background (CMB)

The CMB is the relic radiation from the early universe, originating from the time when the universe cooled enough for atoms to form and photons to decouple from matter. Its nearly perfect blackbody spectrum provides strong evidence for the Big Bang theory and helps in determining key cosmological parameters, including the universe’s overall temperature.

Blackbody Radiation

Blackbody radiation refers to the electromagnetic emission from an idealized object in thermal equilibrium. Its spectrum depends solely on the temperature of the emitting body, allowing scientists to extract temperature information from the shape of the emitted spectrum using theoretical models like Planck’s law.

Wien's Displacement Law

Wien’s Displacement Law relates the temperature of a blackbody to the wavelength at which its emitted radiation intensity is maximum. By observing the peak wavelength of a blackbody spectrum, one can deduce the temperature of the emitting source, which is a central method in astrophysical measurements including studies of the CMB.

Planck's Law

Planck’s Law describes how the radiant energy emitted by a blackbody is distributed across different wavelengths at a given temperature. It provides the theoretical foundation for understanding blackbody spectra and is essential for calculating the temperature from observed spectral data.

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