# Cosmic Microwave Background Radiation [closed]

I'm going through the NRAO Essential Radio Astronomy course and on the section about Cosmic Microwave Background Radiation, it mentions that BB radiation is $T_0 = 2.725 \pm 0.002$ K equating to "frequency of peak brightness" ~ 160 GHz.

Could someone spell out the factors that give this result please? I have seen this figure quoted in another answer to a CMB question, but cannot find the factors.

## closed as unclear what you're asking by Jon Custer, Sebastian Riese, glS, Bill N, ZeroTheHeroJul 18 '18 at 16:02

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• Heh heh. Click bait title? – user93146 Jul 11 '18 at 21:14
• What do you mean by "factors that give this result"? Which result? The temperature is determined by observation. Are you asking how 2.7K corresponds to 160 GHz? – enumaris Jul 11 '18 at 21:31
• Your search might be more fruitful if you ask why a "blackbody spectrum" corresponding to $2.7\,\mathrm{K}$ has a peak frequency near $160\,\mathrm{GHz}$. – dmckee Jul 11 '18 at 22:02
• This is a measured property of the CMB that was measured by the FIRAS instrument on COBE. – Sean E. Lake Jul 12 '18 at 2:52

## 1 Answer

The spectral radiance of a blackbody, $$B_\nu\left(\nu,\,T\right)=\frac{2 h \nu^3}{c^2}\frac{1}{\exp\left(\frac{h\nu}{k_BT}\right)-1},$$ peaks around $\nu=$160GHz when $T=$2.725K. See the Wikipedia article Planck's law.