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A Nebula has bright awesome colors that include red, blue, green, orange, white, etc?

They're result of excitation of electrons.

Is there a clear explanation as to which color is attributed to an atom for Color properties in Cosmos!?

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Yes, nebulae can often have very distinct colours. What produces those colours can depend on what elements are in the nebula material and what the temperature and density are.

Generally speaking, green colours in a nebula are due to forbidden transitions in ionised Oxygen, though can feature the hydrogen $\beta$ Balmer line. Red colours can be due to Hydrogen $\alpha$, but there are also lines due to ionised sulphur and nitrogen that often make contributions.

If you take a spectrum of a nebula it usually completely obvious what elements are responsible, because the spectra consist of very sharp emission lines at the wavelengths that correspond to the well-known electronic transitions in particular species. An example is shown below, which is the spectrum of a typical planetary nebula. Here, the labels mean the following: OIII means oxygen with its outer two electrons removed; NII is nitrogen with its outer electron removed etc., H$\alpha$, $\beta$, $\gamma$ are the $n=3 \rightarrow 2$, $n=4 \rightarrow 2$ and $n=5 \rightarrow 2$ transition of the hydrogen Balmer series. The wavelength scale is in angstroms where 10 angstroms is 1 nm. So 5000 angstroms is the green part of the spectrum, 6500 angstroms is red and 4000 angstroms is blue.

Typical spectrum of a planetary nebula

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