Visualizing Electron Orbitals for a Single Atom

Hey there, I think I can help at least a little bit to get you closer to your answers. Brief disclaimer: my knowledge comes from a year of accelerated gen chem and only that, so I'm by no means an expert yet. Also, summer has set in so I've already begun to forget the specifics of the course, but let me share what I think I know.

  1. Our determination of the probability distributions for electrons comes from manipulations of Schrodinger's equations using models for the ideal behavior of electrons (called the particle-in-a-box model). The resulting wavefunction is an expression of the behavior of the electron as a function of the total energy of the system. The square of this wavefunction gives you the probability distribution for the electron. Adding another electron both screws up the model of the system (one particle in a 2D box) as well as requires a completely different wavefunction for the electrons because the energy of the system must be expressed as the function of the behavior of two particles. Additionally, we know that the two electrons interact with each other (see: VSEPR, for example), so this also explains why the wavefunction and therefore the probability distribution is not simply the addition of that for the two electrons independently. In short, the electrons interact with each other, affecting the probability distribution in the atom.

  2. I believe the above applies to a greater extent as you get bigger atoms with more orbitals that hold more electrons. The probability distribution for atoms with more than one electron don't give the probability distribution for one electron in the multi-particle atom. They give the chance of finding an electron at a certain radius from the nucleus. As you add electrons, the wavefunctions get increasingly more difficult to compute and model. As far as orbital shapes go, you'll have to go somewhere else, because I don't remember enough to be useful.

  3. Speaking of behavior of the electrons ("position") and energies, the number in an orbital represents its relative distance from the nucleus I believe. This does not give an absolute energy level associated with the orbital. I believe we have just found experimentally (and verified using geometry) that in cases like you mentioned with the 4S and 3D orbitals, the 4S orbitals occupy a lower energy (more stable), so those hold the first two electrons on the row containing the transition elements. We know that the 4S is still further out (and if I'm wrong please correct me, that goes for anything in this comment) because for transition element ions (like Co+2), the 4S electrons are the first to be removed.

Hope the information I provided was accurate or even close to it and I helped you come to your answer.

/r/chemistry Thread