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### 2.4: Electron Orbital Model

#### Overview

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations.

#### The Location of an Electron within an Atom Corresponds with an Energy Level and an Orbital Shape

The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells. The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital, termed the 1s orbital, that can hold two electrons. The next shell holds eight total electrons: two in the spherical 2s orbital and two in each of the three dumbbell-shaped 2p orbitals. In higher energy levels, the outermost orbitals—those found in the d and f subshells—take on more complex shapes. A total of 10 electrons can fit within the five d orbitals, and 14 total electrons fit within the seven f orbitals.

Orbital diagrams can be used to visualize the location and relative energy levels of each electron in an atom. Within each shell, electrons have a rising level of energy. The s subshell has the lowest amount of energy. Electrons in the p subshell have somewhat higher energy, followed by the d and f subshell if they are present.

#### The Bohr Model Introduced the Concept of Orbitals

We have seen that electrons in different orbitals have different energy levels. How do we know that there is energy in the electrons at all, much less that electrons can have differing amounts of energy? In 1913, Niels Bohr was able to experimentally determine how much energy was gained and lost when electrons changed orbitals in an atom of hydrogen and other ions with a single electron. Combining the results of his experiments with prior knowledge of a positively-charged nucleus from the work of Ernest Rutherford, Bohr developed the first model of electron orbitals.

When electrons gain energy, they enter an excited state and jump to higher orbitals. Energy can be added to electrons in the form of heat or light, and when they lose that energy rapidly, they fall back from the higher orbital and emit a particle of light called a photon. The color of the emitted photon corresponds to a specific amount of energy so that it can be quantified by a spectroscope.

Bohr was able to determine the energy contained in principal energy levels—also referred to as shells—by heating hydrogen. The additional heat energy forced the electron to jump up from the first energy level to higher levels. Bohr then measured the wavelength of light that was emitted when the atoms cooled down again.

#### The Quantum Mechanical Model of the Atom

Bohr’s model of electron orbitals assumed that electrons orbited the nucleus in fixed circular paths. While his experiments were accurate for hydrogen and hydrogen-like ions with a single electron, he could not predict the electron configurations of other elements. There had to be additional factors influencing the physics of subatomic particles.

In 1926 Erwin Schrödinger expanded Bohr’s model of energy levels and developed the model of atomic orbitals that is still accepted today. Schrödinger took a number of other discoveries into account regarding the physical behavior of electrons that were made by scientists in the early 1920s. His quantum mechanical model accurately predicts the electron configurations of elements with multiple electrons. One fundamental change in Schrödinger’s model is the assumption that electrons travel in a wave motion that is affected by the positive charge of the nucleus. Because of this, the orbitals that we speak of today are cloud-like areas where electrons are most likely to be found rather than fixed circular paths as Bohr proposed. Another critical distinction is the division of Bohr’s energy levels—shells—into smaller categories—subshells and orbitals.

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