Explain which electron transition in the hydrogen atom produces the red line in the hydrogen atom emission spectrum.
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Emission of photons from an element occurs when an electron in a high energy state drops down to a lower energy state. This happens instantaneously with no interim position between states, and the levels that it drops from and ends up at are very specific for each element. This drop in electron energy means, since energy is conserved, energy is released, in this case as a photon. The frequency, and therefore the colour, of the photon, is determined by the energy through E = hf.
In this case, we are dealing with hydrogen. The line is said to be red, so photons produced are in the visible spectrum. In hydrogen this is the Balmer series, where an electron drops down to the second energy state, or n=2. All the other lines produced are in the blue end of the spectrum. Blue light has a higher frequency than red light, and thus more energy, so the single red line, having the least energy, must have been produced from the least drop in energy by the electron. The smallest drop possible in the Balmer series is n=3 to n=2, therefore that electron transition produced the red light.
Awesome answer Michael. Well done.