Bohr (1913), proposed a model of the hydrogen atom that made no intuitive sense: had a short life in the history of Physics: and was a ground breaking achievement for which he banked the 1922 Nobel prize in Physics.
1 Many years earlier a German by the name of Rydberg had written down an empirical formula which gave the wavelengths of the emissions of a hydrogen atom.
... where n and m are integers.
For example n = 1 and m = 2, 3, 4, etc. gives a ladder of wavelengths.
... n = 2 and m = 3, 4, 5, etc. gives a second ladder and so on.
The reason for the success of his slightly odd formula was not known, but any theory of the hydrogen atom would be expected to give the formula, since it is correct, to within a fraction of one percent.
2 Suppose an electron orbits the nucleus. The centripetal force is the Coulomb attraction.
3 The total energy of the 'orbiting' electron (PE + KE ) is constant, equal to....
Electron energy is inversely proportional to the radius of a circular orbit. In classical physics the electron can have any energy. Orbits are elliptical and unstable because the accelerated electron emits energy as radiation.
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If we are to have orbits of just the right energy, to fit Rydberg's formula, we must have some ... ... New physics. |
A positive grid is added to a cathode ray tube between the cathode and the anode. The tube is filled with low pressure gas. The tube was not completely evacuated.
The positive voltage on the grid is less than the anode voltage. As the grid voltage is increased, the anode current increases as expected, but the voltage-current curve is found to be, not the expected curve but a wavy line, with peaks that are evenly spaced.
Other gas fillings (mercury vapor and neon etc.) give similar peaks at different separations. The gas in the tube causes the anode current to vary in an interesting way. For mercury vapor the peaks are separated on the horizontal voltage axis by 4.9 Volts (see below).
Explanation
As electrons are accelerated towards the grid they reach a particular kinetic energy, and begin to transfer their energy by collisions to gas atoms, that became excited, and then an instant later, emit the energy as light photons. The current drops each time the electrons slow down (lose energy) as they excite gas atoms. For this reason the peaks are equally a spaced and at different spacings for different gasses.
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A neon filled tube with a grid voltage of 60 Volts is shown with three glowing regions.  The glowing bands are due to excitation when electrons have ~18 eV of kinetic energy. |
The Frank-Hertz demonstration, as it is now called, shows that there are energy levels in atoms. The atoms absorb energy from moving electrons and release that energy as light photons.
Hot gas (flames) emit particular wavelengths of light as excited atoms return to lower energy states. The electrons in the outer shells move from one stable condition to another, emitting photons of particular energies as they do so.
Large volumes of gas or plasma (the atmosphere of the Sun) absorb particular wavelengths as light passes through. The continuous spectrum of the sun is crossed by dark absorption lines named after Fraunhofer.
Erwin Schrödinger (1923) put the atomic physics picture on a better conceptual footing by describing the energy levels in atoms as wave functions. Three dimensional standing waves around the nucleus, called spherical harmonics. The simplest harmonics are spheres, more complex ones have other shapes. Remarkably, he was able to represent the energy levels and to reproduce Rydberg's formula for the hydrogen emission lines without the impossibility of orbiting electrons.
There was much argument as to what his wave functions might represent. The most popular interpretation - still in vogue today - regards the wave functions as probability waves. The amplitude of the wave is the probability of finding the electron at that point. The electron is no longer though of as a particle with a location. At a particular radius (in the spherically symmetric ground state) it is equally likely that the electron may be found in any direction. The electron is distributed into a shell of charge.
This interpretation is consistent with Heisenberg's principle. The angular momentum of the electron is known precisely (zero) but the direction is, in principle, unknowable.