Electrons, Protons and the Coulomb Force

Before modelling protons and electrons under the coulomb force, a quick note about time scales and distance scales. Distances on the atomic scale for protons and atoms are often measured in picometers (10‾¹²), where the Bohr radius is 53pm. For electrons, distances can go as small as the Lorentz radius of 3 femtometers (10‾¹⁵). For tracking electrons, attoseconds (10‾¹⁸) is […]

Keeping Track of Electron Orbitals and Energy Levels

In his Autobiographical Notes in 1949, Einstein wrote of the special theory It is striking that the theory introduces two kinds of physical things, i.e., (1) measuring rods and clocks, and (2) all other things, e.g., the electromagnetic field, the material point, etc. In the last blog entry, we set the measuring rods to picometers (10‾¹²) and our clocks to […]

The Helium-Neon Laser

The last blog talked about no longer tracking electrons through the coulomb force, but rather, thinking of an electron as being confined to a specific area around the nucleus at a specific energy level. The electrons are so fast and light compared to the nucleus of an atom that we need a better way to model what is going on. The quantum […]

The Ideal Gas Law

Click here to to see the animation of molecules in motion. The Ideal Gas Law states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional. To model the normal air we breath at 20°C we are dealing with free flowing molecules travelling in the range of a few nanometers per picosecond. We chose […]

Spherical Harmonics and Quantum numbers

Atomic orbitals are calculated from mathematical wave functions that predict the probability of finding an electron or a pair of electrons in a specific region around the atom’s nucleus. Quantum mechanics tells us that electrons in an atom possess four quantum numbers that determine what energy level the electron is at. They are: Orbital, n=1,2,3…; Azimuthal, l=0,1,2…n−1; Magnetic, ml=−l,−l+1…0…l−1,l; and finally Spin, ms=−1/2,1/2. The […]