What force accounts for the shapes of electron shells?

Question

I've taken high school physics, so I have a gentle grasp of the basics. I know a little about quantum mechanics and the idea of probability of position.

So, the shape of the areas in which electrons can be found at each shell is unusual- like the teardrop shape of the p shell- and clearly they aren't in orbit like most models would lead you to think. But, I have no idea why it's like that.

So, what keeps the electrons A.) from getting closer and sticking to the oppositely-charged protons and B.) in the particular areas we are likely to find them in? How?

Answer 1

A) well the electron also has a very high velocity. its basically like how the moon orbits the earth. an electron is continuously falling towards the nucleus of an atom, but its sideways velocity causes it to keep missing it.

B) according to quantum mechanics, electrons arent just particles. they can be expressed as wave functions also. when the crests of two waves line up they cancel out, its called interference. since the electron is a wave, and it orbits in a circle, it is possible for the crests of the wave to meet and for the electron to essentially cancel itself out. to prevent this, the electron orbits in specific locations around the atom, these are electron energy levels, or shells.

Answer 2

The only actual force in play is the Coulomb interaction between the nucleus and the electrons.

Now things are going to get pretty incomprehensible if you only understand classical mechanics.

According to quantum mechanics, the electron doesn't have any fixed position and momentum.  The electron is governed by a wave function which is a solution to a differential equation called Schrodinger's equation.  These solutions have discrete energies and angular momenta.  It's sort of like how a wave on a string or an organ pipe can only resonate at certain discrete frequencies.  So anyway, if you decided to look for it, the electron would be somewhere in this cloud.  The cloud is very big compared to the nucleus, so although the electron can be found in the nucleus at times, it doesn't stick there.  It's too busy buzzing around the entire cloud to be stuck in one little place.  Even if that one little place is the single most likely place for it to be, which it is for s orbitals, it is still just a little place in a big cloud.

B)  Don't put too much stock in those teardrop shapes.  They are tools of the chemists.  S orbitals are spherically symmetric.  The sum of all the p orbitals (and d orbitals and all the rest) is spherically symmetric.  But you can break the orbitals out in different linear combinations.  (Any linear combination of wave functions with your desired qualities is itself a good wave function).  So the chemists like those teardrop shaped ones because they are useful for bonding.  Physicists tend to use the direction of angular momentum to break them out, which gives you different-looking orbitals.  As for where you find the electrons, it goes back to the wave function.  For the s orbitals, the most likely spot to find the electron is at the nucleus and the probability falls off from there.  For the p and d and higher angular momentum orbitals, their angular momentum provides a centrifugal pseudo-force that pushes them away from the center, so they are more likely to be found some distance away.

Before you can understand too much more than this, you have to go to college and learn multi-variable calculus and differential equations so you can actually look at the Schrodinger equation and make sense of it.

Answer 3

Quantum mechanics isn't about forces. In a quantum mechanics class, we call "force" the "F-Word." Force is a macroscopic limit of the correct quantum interactions of particles, which can only be described in terms of energies and potentials, not forces. So it is not a force that makes electrons in atoms do what they do; it is the spherically symmetric nature of the electric potential.

A) Electrons cannot get closer to the nucleus because there are no solutions to the Schrödinger equation in there, and all motion must be a solution of the Schrödinger equation. That all motion must be a solution to the SE is a postulate of quantum mechanics, based on observations such as this.

B) The shape of the orbitals is also due to the solutions of the SE. The SE is a wave equation, whose solutions are always waves. In this case, because the electric potential (which keeps the electrons in orbit) is spherically symmetric, the solutions of the SE are spherical harmonics. Spherical harmonics are the equivalents of sines and cosines when mathematics is done on a spherical membrane instead of a number line. If you pluck a string, the string vibrates with waves that look like sines and cosines. If you beat a spherical drum, the drum vibrates with waves that look like spherical harmonics. These spherical harmonics have the familiar s, p, d, f, etc., shapes that you're thinking about. Incidentally, if you solve the SE for electron motion on a string, you get sines and cosines.