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I was studying oxidising flames and realized that sodium burns with a bright yellow flame the wavelength of which is around 588 nm. Then I searched for emission spectra of sodium and found that the lines around 588 nm are the most intense ones, so it appears yellow. The same happened with potassium.

But when I arrived at hydrogen, I knew it burned with a pale blue flame, but its emission spectral lines were most intense in the red region. So why does it still gives a blue flame?

Emission spectral lines of hydrogen

As you see, it emits blue light too, but the red one is the most intense and so electrical discharge of hydrogen emits red light. But its oxidising flame is pale blue.

Would it burn with a red flame at higher temperature or something like that or are spectral lines not related to flame colours?

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It is a very interesting question, but comparing a combustion spectrum with an atomic emission one is like comparing apples and oranges. A flame is a luminous gas phase chemical reaction where the hydrogen atoms are combining with oxygen atoms. It is a chemiluminescence phenomenon. A discharge tube emission is an atomic emission.

You posted a picture of a hydrogen spectrum from a discharge tube which consists of discrete lines in the UV, visible, and IR regions. In the same way, the hydrogen-air flame has an emission in the ultraviolet, visible and in the IR. The blue flame is not a line spectrum, as you might speculate. It is a continuum (broad band), which indicates that this is due to molecular emission in the flames, not from hydrogen atoms! This is in contrast with the alkali metals whose compounds easily atomize in the flame.

Also note that what may appear to us as a single color, like blue, is rarely a single wavelength.

There is a beautiful article by R.W. Schefer , W.D. Kulatilaka, B.D. Patterson, and T.B. Settersten on Visible emission of hydrogen flames, Combustion and Flame 156 (2009) 1234–1241. Go to Google Scholar and find it; it is open access on Google.

Look at their experiment: They view the "blue" hydrogen flames by various optical filters which block or pass certain wavelengths. See many colors are present in the "blue" flame of hydrogen. In fact most of the emission is in the ultraviolet region.

Flame

Direct flame luminosity photographs in a laminar, diffusion H2-jet flame. (a) Unfiltered, f /2.4 aperture; (b) short-wavelength pass filter with 550 nm cutoff wavelength, f /2.4 aperture; (c) long-wavelength pass filter with 530 nm cutoff wavelength. Images taken at f /2.4 aperture with 90-ms exposure time. Fuel jet exit velocity is 47 m/s with a coflow air velocity of 0.57 m/s. Reynolds number = 837.

Most of the emission is in the UV and infrared as you can see from the spike near 300 nm and intense band after 700 nm. Most people cannot see beyond 700 nm. The infrared emission is due to excited water molecule or perhaps its fragments.

Spectrum

Note: The above spectrum consists of two parts, UV on the left, and visible extending from $\pu{350 nm}$ to $\pu{850 nm}$ on the right hand side, recorded separately. For this figure, the later was amplified by a factor of 6.5 with respect to the OH in the ultraviolet.

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    $\begingroup$ I think the subsequent figure (ars.els-cdn.com/content/image/…) is actually the one you want to demonstrate why the flame is blue. While interesting, the UV and IR spectra have little to say about human color perception. $\endgroup$
    – Xerxes
    Apr 12 at 14:00
  • $\begingroup$ Are you sure it is open access? Doesn't it just point to sciencedirect.com where only the abstract is available ("Purchase PDF" and "Access through your institution")? $\endgroup$ Apr 12 at 19:31
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    $\begingroup$ If you search Google with this title, the first result should be the pdf of this article. It is hosted by zenodo.org "Zenodo is a general-purpose open-access repository developed under the European OpenAIRE program and operated by CERN." I think this is a legit website as per Wiki information. $\endgroup$
    – M. Farooq
    Apr 12 at 19:36
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    $\begingroup$ @PeterMortensen If you use Firefox with its add-on unpaywall, then Elsevier's landing page of this publication is marked on the right hand side by an open padlock on green background. While this then links directly to the pdf, just remove the two last layers of this string https://zenodo.org/record/1258847/files/article.pdf to reach zenodo's landing page including the copyright note (here: Creative Commons Zero v1.0 Universal) for this work. $\endgroup$
    – Buttonwood
    Apr 13 at 13:09

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