# How are line spectra explained after rejecting/improving Bohr's theory?

I learned that Bohr explained line spectra by postulating that electrons can only be at certain discrete distances from the nucleus. Later, this theory was refuted/improved by de Broglie and Schrödinger. Since their theories, electrons were seen as standing waves and we can only know where they will probably be. The regions with $$90\%$$ probability are called orbitals. But how can line spectra be explained if electrons are not restricted to discrete distances but rather to orbital regions?

By the way, am I getting the idea of orbitals correctly ? Is it correct to see it as a region with a high probability of finding an electron as a standing wave?

Since their theories, electrons were seen as standing waves and we can only know where they will probably be. The regions with $$90\%$$ probability are called orbitals.

Not quite. The orbital is the standing wave itself.

But how can line spectra be explained if electrons are not restricted to discrete distances but rather to orbital regions?

The discreteness of line spectra arises in the same way that only a few frequencies can sustain a standing wave in a confined mechanical system such as a drum or the 3D volume inside a trumpet - the mathematics is identical, as are the mental constructs used to explain them, except that you need to understand that you're now doing wave mechanics instead of point-particle mechanics.

A couple more things that fall out from the way you've posed your question:

• It's important to note that as far as the positions of the lines in the spectrum of atomic hydrogen are concerned, the Bohr model gives exactly the same answers as full-blown quantum mechanics as introduced by Schrödinger.
• On the other hand, QM goes beyond what the Bohr model can say for atomic hydrogen, and it allows you to calculate things like the relative strengths of the different lines and their natural widths, which the Bohr model is completely silent about.
• Moreover, the Bohr model is essentially limited to hydrogen and hydrogenic ions, which is an extremely restricted set of systems. Full-blown QM can go beyond this to treat helium and any larger atom or molecule that you care to throw at it.

But how can line spectra be explained if electrons are not restricted to discrete distances but rather to orbital regions?

It's because the electrons are restricted to discrete energies, not distances. This can be properly explained with quantum mechanics, but basically, electrons can only have "pieces" of energy. Each of these energy levels is associated with different orbitals.

When the electron makes a transition from one energy level to a lower one, the atom emits a photon, or light, with an energy equal to the amount that the electron lost. By measuring the energy of the emitted photon, we can find the spectral lines.

Now, most of the time, a higher energy level will mean that the electron is, on average, further away from the nucleus. But the picture that an electron "jumps" down from one orbital to the next is not what's actually going on.

Is it correct to see it as a region with a high probability of finding an electron as a standing wave?

Yeah. This is pretty much on point.

• Thanks for your answer. But how is it that the electron can have the same energy in different points in space? – Sudera Nov 18 '18 at 19:19
• "the electron" is actually an "electron cloud", or orbital, which you already seem to understand. The orbital is a probability density over all space which is associated with a discrete energy. The electron is not a particle. – Hanting Zhang Nov 18 '18 at 19:23