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If you had a single hydrogen atom, and you watched for a single transition, then yes, you would only see emission at a single frequency. There would be one line in your spectrograph so to speak. But rarely do you have just one atom. And quite often an atom undergoes multiple transitions while you are watching it. When looking at a large ensemble, whether it ...

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There is no luck involved. Quite the opposite. Firstly, as many of the comments say, spectal lines arise in a very wide range of frequencies well outside the visible range. Secondly, and IMO more importantly for this answer, evolution is NOT random. And we see in the visible range because: "Most" of the Sun's radiant energy is in this band, in the sense ...

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The Balmer series for hydrogen is an example with some visible lines, and some lines outside the visible spectrum. On the other hand, the Lyman series for hydrogen is completely outside the visible spectrum. Since every element has an infinite number of spectral lines, it would instead be very unlucky if they all somehow fell outside the visible spectrum.

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Because the electron's initial state is a superposition of states with different energies, the electron does not have definite energy. Measuring its energy, you would find either $E_{4s}$ (with probability $\frac{x^2}{x^2+(1-x)^2}$) or $E_{3p}$ (with probability one minus that). Since it's energy isn't a definite number, we have to resort to talking about ...

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A "sharp" tip typically has a finite curvature; there will be a very small part of the "tip" that is therefore angled at such a way that light will be reflected off it. The sharper the tip, the smaller the radius of curvature, and the smaller the "twinkle" or glint. The second effect is diffraction: Light that passes an object will be diffracted. For ...

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