Electronic Structure of Atoms: Intro and Visualization

Electromagnetic Radiation can be characterized by wavelength, frequency, and speed. This is typical wave-like behavior, and radiation was long-believed to behave solely as waves. However...

• 1901: Max Plank found that atoms can only adsorb and emit energy in distict quantities; this showed that energy displayed particle-like properties.
• 1905: Albert Einstein suggested that energy itself is quantized and can be viewed as a string of particles called photons. He established that energy has mass.
• 1922: Arthur Compton verified that photons have mass through experiments.

Thus, the dual nature of matter, wave-like and particle-like, had been established. The race to explain this was on...

Hydrogen atoms were known to emit specific wavelengths of light after being excited. In 1913, Neils Bohr, focusing on the particle properties of electrons, constructed a quantum model to explain this. He proposed that electrons orbited the nucleaus at specific radii, also called energy levels.

Electrons required specific (quantized) amounts of energy to move from one energy level to another, and emitted characteristic amounts of energy when returning the ground-state energy levels.

His model predicted that electrons were more tightly bound when they were closer to the nucleus, and that atoms emitted energy when electrons dropped energy levels, moving towards the nucleus.

With a lot of assumptions and adjustments, the Bohr Model fit Hydrogen pretty well, but failed for all other atoms. It was soon recognized that it was fundamentally wrong, and a new approach was needed.

Electron visualized as a standing wave

In the mid-1920s, Erwin Schrodinger, building on the dual nature of matter, began focusing on the wave-like properties of the electron. By visualizing electons as standing waves (like guitar strings) instead of "orbiting" particles, the distinct energy levels observed by experiments could be explained.

In the diagram to the bottom-left, the circumferences of the different circles represent possible energy levels for the electron to occupy. Given a particular wavelenth, only certain circumferences line up properly. Other ones result in destructive interference and are not "allowed."

Using this idea, Schrodinger developed a mathematical model based on wave mathematics to describe the position of electrons in an atom. For a given atom, Schrodinger's Equation has many solutions, and these different solutions are called orbitals. These orbitals do not describe actual orbits like Bohr's model, but, instead, solutions to a mathematical equation.

The standing wave diagram is a visualization of why, if electrons have wave-like properties like wavelength, only certain orbitals are allowed. It is not meant to say that electrons move in wavy orbits around the nucleus.

The dotted images correspond to the probability distribution for a particular solution (orbital) to Schrodinger's Equation. Based on the probability of where the electron might be, a boundary can be drawn, and a "shape" to the orbital can be described. While different atoms have different solutions to the Schrodinger Equation, many of the solutions look similar between atoms, and these orbitals have specific names. The ones above and below are called p-type, and the ones to the left are called d-type.

p-type orbital for Boron

2 overlapped p-type orbitals for carbon. The different orbitals are different colors (one is horizontal and one is vertical).

The many solutions to Schrodinger's equation can be classifed by the shape their probability distributions take, called orbitals, like s, p, and d-type, as shown above. Most orbital types have several possible orientations too, as seen with the vertical and horizontal p-type orbitals shown with Carbon above.

In addition to orbital type and orientation, each orbital can exist at several energy levels. Orbitals of different energy levels have the same general shape, in terms of boundary surface representation, but are bigger at higher energy levels.

In addition, the probablity distributions for orbitals at higher energy levels show "dead" spots, called nodes. This doesn't change the overall shape we imagine the orbital has, but is an interesting phenomenon.

Note: Not all orbitals exists at all energy levels. There is no 1st-level p orbital, or 1st- and 2nd-level d orbital.