# Development of Quantum Physics VII – Atoms Are Choosy When It Comes to Wavelengths

In 1847, when Max Planck asked his physics teacher about the career outlook and the job opportunities with a degree in physics, he was advised against going into physics. (“In this field, almost everything is already discovered, and all that remains is to fill a few holes.”) One of this “few holes” was the issue of the ultraviolet catastrophe of the black body radiation. Planck managed to fill this hole by making use of his quantum hypothesis. Funnily enough, as it turned out, this problem was anything but insignificant and small – its solution rather upends our whole physical conception of the world and lays the foundation of a new extensive and very accurate theory: Quantum physics.

If Planck’s former teacher had known that his student will become one of the most famous physicists of all time, I think he wouldn’t have discouraged him from studying physics.

Max Planck in Munich, 1847
(Source: Wikimedia Commons)

Countless new ideas and concepts followed Planck’s quantum hypothesis, as already mentioned in the previous articles of this series. For instance, we discovered that light consists of photons (“wave packets”), that “particles” (such as electrons) can be described using wave characteristics, that, however, this resulting matter wave represents just the probability of the particle to be found at a certain point in space and time, and that there exist fundamental limits in simultaneously determining a particle’s position and momentum.

Has anyone noticed that, although we thoroughly fiddled with the microscopic characterization of light and matter, we didn’t dwell on how matter actually looks like? Or, to put it differently: How should we think of an atom? How can we figure it to ourselves? Today we will enter into this question.

(Most of the previous parts of this series of articles are already linked in the introduction above. Nevertheless, you can find all the other posts in this neatly arranged list.)

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Of course, another whole series of articles could be written about the development of the conception of an atom – many different ideas and concepts were brought into existence and were experimentally debunked later. Hundred-odd years ago, we realized that atoms have to consist of a nucleus and a shell. Almost all the atom’s mass is concentrated into the nucleus which has a radius smaller than $10^{-14}$ meters. While the nuclear charge is $+Z\cdot e$ ($Z$ times the elementary charge $e=-1.602\cdot 10^{-19}$ Coulomb), the shell is made of $Z$ electrons with a charge of $-e$. The masses of these electrons are enormously small compared to the nuclear mass and they occupy a space which is roughly $10^{12}$ to $10^{15}$ times the size of the nucleus.

But how does the electron shell look like? Are the electrons somehow statistically distributed around the nucleus? (Due to the attracting electrostatic force between the positively charged nucleus and the negatively charged electrons, this configuration wouldn’t be stable over time.) Or do the they move around the nucleus by any means? (If so, the electrons must radiate energy, according to classical electrodynamics. This configuration, too, would be unstable.)

Furthermore, other experimental observations had to be taken into account by potential new atom models, such as the fact that atoms absorb or emit radiation (or light, if you will) in specific wavelengths only. If you plot the absorption of some type of atom against the wavelengths, you get the characteristic absorption spectrum. The same goes for emission – what you get in this case is the typical emission spectrum of the atom.

We experimentally found laws for these spctra as follows:

• Wavelengths which can be absorbed by an atom can equally be emitted by the atom, if it is supplied with a corresponding amount of energy.
• For every atom, there is a very characteristic absorption and emission spectrum. This spectrum is unique for the given type of atom. (It is due to this fact that wonderful things like spectroscopy are possible after all.)
• No matter how accurate our measuring instruments are, the spectral lines always show an unlasting intensity distribution (= the spectrals lines always have a certain “width”). Therefore, the radiation emitted by atoms never consists of a single wavelength only – it is never strictly monochromatic.
(I won’t explain the reason for this phenomenon here, because it would require some mathematics and go beyond the scope of this article. Nevertheless, here’s one (of several) reasons why the spectral lines cannot be arbitrarily sharp: The always existing jitter and shaking of atoms cause small frequency shifts in the emitted radiation because of the Doppler effect.)

Here’s the emission spectrum for the simplest atom, the hydrogen atom:

Visible spectrum of hydrogen.
(Credit: Jan Homann. Source: Wikimedia Commons)

Johann Jakob Balmer found a simple law (“Balmer series“) for this series of spectral lines in 1885.

A while later, though, Theodore Lymann and Friedrich Paschen found other series of spectral lines which can also be described in terms of Balmer’s law. (You just have to insert different “reference points” into the forumula.)

Emission spectrum of hydrogen, on a logarithmic scale (schematically).
(Credit: OrangeDog, via Wikimedia Commons)

How can we theoretically explain all these experimental results? How does an atom have to look like in order to generate the observed spectra?

Many different models were worked out by many different people. But none of these models was able to combine and consistently describe the observations.
Albeit, in the year 1931 a physicist was able to create an atom model which was indeed able to produce the experimental results from theory.

I will save the description of this model until the next article. But one thing can be already said at this point: What’s nice about his model is that it is a quite intuitively accesible one, even if we spare the mathematical details. If we consider the mathematics behind this model though, we will find it not too hard to understand. (I’ll do the maths in a seperate article which you can easily skip if you aren’t into fiddling with symbols and numbers. 😉 )
Anyway, as elegant and aesthetic this model may seem, it’s not the whole truth. By saying this, I’d like to point to the next article of this series…

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