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Regarding the Fine Structure Constant in the spectral emission lines of a hydrogen atom, does the narrow gap/black line represent 1 out of 137 slices or possible steps of something?

In the color lines of a spectrograph and what seems to be an area with a certain color, zooming in shows that this color is delicately split in half by a black vertical hairline, on one side it's the emission of photons of color by a hydrogen atom with a spin up electron, on the other it seems to be the same color but it's a spin down electron.

Whenever I hear that gap mentioned, 1/137 is invoked, but I'm not sure precisely what that means, and I'm visualizing that the color of the spectral emission can be divided or deconstructed into a total of 137 vertical lines, and the one in the middle is black.

Maybe it represents 1/137 of a photon's wavelength at a certain color?

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