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I heard the CMB is the electromagnetic radiation from the big bang. It is 13.7 b years old but isnt it only in the microwave range of the spectrum (300MHz - 300GHz) . Can a FM radio receiver (87-108MHz)pickup the noise from the CMB ?

I don't think it has neat boundaries...

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So Cosmic Microwave Background radiation corresponds very neatly to a blackbody spectrum of temperature 2.7K. This is an image which shows data collected by satellites: enter image description here

The key thing to understand is that it is a spectrum, not a set of discrete frequencies that are present. So to answer your question, theoretically yes a FM radio receiver (87-108MHz) could pickup the noise from the CMB, but since CMBR has a very low intensity in the first place, as well as radio waves making up only a tiny part of CMBR's spectrum, in practise it's unlikely.

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The CMB has a blackbody spectrum at T = 2.7 K, which peaks in the microwave range ($\lambda \approx 2\,{\rm mm}$). The intensity of the blackbody spectrum is given by Planck's Law: $$B(\nu,T) \propto \frac{\nu^3}{e^{h\nu/kT} -1},$$ which decays but is nonzero at lower frequencies.

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yes, it does. if you have an old analog television receiver, you can tune it to an unused channel in the UHF band and look at the random static on the screen. about 10% of that static comes from the CMB.

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    $\begingroup$ I heard it was 1% $\endgroup$ – ObsessionWithElectricity Sep 5 '18 at 18:31
  • $\begingroup$ could be. I can't remember the original reference. $\endgroup$ – niels nielsen Sep 5 '18 at 22:33

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