When Did We Last Get a Glimpse of the Big Bang?

[PeterDonis]

when the temp cooled and the universe became transparent i read around 57,000 years after the big bang what would the wavelength of the CMB be then?

As phinds says, this event, which is called "recombination" (see below), was a few hundred thousand years after the Big Bang. It was also the event at which the CMB was formed; "the universe became transparent" was the condition that had to be met for the CMB to exist--before that, radiation emitted by the matter in the universe was quickly re-absorbed because the matter was ionized plasma. "Recombination" means the electrons and ions in the plasma came together to form neutral atoms; that was what made the universe transparent to EM radiation and allowed the CMB to exist.

The wavelength of the CMB at this point, when it was first formed, was determined by the temperature at which recombination occurred, which was a few thousand degrees Kelvin. That temperature determined the average energy of the radiation that formed the CMB when the universe became transparent, and the average energy in turn determined the frequency and wavelength of the radiation. We can estimate what that wavelength was by measuring the redshift of the CMB, which turns out to be about 1000; so the wavelength of the CMB when it was formed was about 1000 times shorter than its wavelength now. Its wavelength now is about 10 mm, so its wavelength then would have been about 10μm, or about $10^{-5}$ meters.

 

[rootone]

Long wavelength infrared.
I was expecting something more spectacular!

 

[PeterDonis]

Long wavelength infrared.
I was expecting something more spectacular!

Remember that mine was a very, very rough calculation. Also remember that the CMB is not just one wavelength; it's a black-body spectrum at a particular temperature, which today is about 2.7 K, and when it was formed was a few thousand degrees K. The wavelength I quoted was just the wavelength at which the spectrum peaks; there is significant radiation at a fair range of longer and shorter wavelengths as well. When the CMB was formed, there would have been a significant component in the visible range; something like a star rather cooler than the Sun.

 

[rootone]

Thanks, yes I figured it would be something like that, so in principle the recombination event would actually have been visible to some hypothetical human observer.
Probably they could see light/feel heat in the same range as that of the embers of a small wood fire.

 

[bapowell]

Long wavelength infrared.
I was expecting something more spectacular!

Yeah, keep in mind that a quick order of magnitude guess assumes that photon energies would be in the neighborhood of the hydrogen ground state energy, which are in the UV part of the spectrum. So it would be at most that spectacular. In actuality, one finds that the photon energies peak a few orders of magnitude less than UV, into the IR as PeterDonis says.