# White hot hydrogen gas, like that during a big bang

Difficult to know for certain which field this is. According to what I can discover about it, the big bang explodes into being as white hot hydrogen gas, millions of degrees hot.

I'm okay with that my question is what colour would it fade to as it cools down? Is there a spectrum I can refer that would illustrate that. I've seen such diagrams for metals as they cool down.

Difficult times people, thank you for your time and input, stay safe. Cheers!

• I don't know how the spectra of gases at millions of degrees look like, but at cooler temperatures, say, 10000 K, the spectrum of the sun is a good example. What did you read about the metal spectra ? – M. Farooq Mar 30 at 3:49
• Hey thnx. I have a chart somewhere showing the colours white hot metal fades to as it cools down but that of course is metal. It first fades to a deepr white then yellow and then shades of red colours. Was wondering about white hot gas. It's a tricky one! Cheers – Chess Wade Mar 30 at 4:38
• I guess black body radiation with given temperature will make a good approximation. – Ivan Neretin Mar 30 at 5:01
• How soon after the big bang? See e.g. en.wikipedia.org/wiki/Recombination_(cosmology) – Buck Thorn Mar 30 at 11:33
• Hydrogen gas cannot be millions of degrees: the bond dissociation energy is 436 kJ/mol, so it will dissociate to atoms as you increase the temperature. Then the ionization energy of a hydrogen atom is 13.6 eV, so all you have is protons and electrons. The recombination link by @BuckThorn is worth reading. – Ed V Mar 30 at 13:30

(This might get more/better answers on Physics Stack Exchange)

At the high temperatures of the early Big Bang, you have individual protons and electrons, not hydrogen atoms and molecules. This is because the $$kT$$ thermal energy is much, much more than the binding energy of the hydrogen atom.

In that case, the moving individual charges create a continuous black body spectrum:

(from Sun.org)

The light will look like a 10,000K source: a bit on the blue side. But most of the energy will be at wavelengths much shorter than visible light. The Wien displacement law shows that:

$$\lambda_{\rm{peak}} = {{b}\over{T}} = {{3\times 10^{-3}m \cdot K}\over{1\times 10^6 K}} = 3\times 10^{-9}m$$

A 3nm wavelength corresponds to soft X-rays (or perhaps the very hardest ultraviolet light).

You'll note that the vertical axis below is logarithmic. At 100X temperature to the 10000K like, the peak will be at the shorter (left) wavelengths of X rays, but also much higher. The energy flux goes as $$T^4$$, so a 100X temperature is a factor of $$10^8$$ in intensity: There will be a lot of X rays at these early temperatures.