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It is said that the cosmic microwave radiation (CMB) was formed when the universe was 379,000 years old. How is this calculated?

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We observe the temperature of the CMB as a ~2.7 K blackbody, but that's the redshifted version we observe. The CMB is also know as the "surface of last scattering" at the point of recombination when nuclei and electrons combined to form neutral atoms the universe went from opaque to transparent.

This happens at a temperature of ~3000 K. From this we can estimate the redshift (z~1100) of the CMB which corresponds to an age given our cosmology.

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