Atom

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Electron Orbitals and Shells

Physicists call the region of space an electron occupies in an atom the electron’s orbital. Similar orbitals constitute groups called shells. The electrons in the orbitals of a particular shell have similar levels of energy. This energy is in the form of both kinetic energy and potential energy. Lower shells are close to the nucleus and higher shells are farther from the nucleus. Electrons occupying orbitals in higher shells generally have more energy than electrons occupying orbitals in lower shells.

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Differences Between Orbitals

The wavelike nature of electrons sets boundaries for their possible locations and determines what shape their orbital, or cloud of probability, will form. Orbitals differ from each other in size, angular momentum, and magnetic properties. In general, angular momentum is the energy an object contains based on how fast the object is revolving, the object’s mass, and the object’s distance from the axis around which it is revolving. The angular momentum of a whirling ball tied to a string, for example, would be greater if the ball was heavier, the string was longer, or the whirling was faster. In atoms, the angular momentum of an electron orbital depends on the size and shape of the orbital. Orbitals with the same size and shape all have the same angular momentum. Some orbitals, however, can differ in shape but still have the same angular momentum. The magnetic properties of an orbital describe how it would behave in a magnetic field. Magnetic properties also depend on the size and shape of the orbital, as well as on the orbital’s orientation in space.

The orbitals in an atom must occur at certain distances from the nucleus to create a stable atom. At these distances, the orbitals allow the electron wave to complete one or more half-wavelengths (y, 1, 1y, 2, 2y, and so on) as it travels around the nucleus. The electron wave can then double back on itself and constructively interfere with itself in a way that reinforces the wave. Any other distance would cause the electron to interfere with its own wave in an unpredictable and unstable way, creating an unstable atom.

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Principal and Secondary Quantum Numbers

Physicists call the number of half-wavelengths that an orbital allows the orbital’s principal quantum number (abbreviated n). In general, this number determines the size of the orbital. Larger orbitals allow more half-wavelengths and therefore have higher principal quantum numbers. The orbital that allows one half-wavelength has a principal quantum number of one. Only one orbital allows one half-wavelength. More than one orbital can allow two or more half-wavelengths. These orbitals may have the same principal quantum number, but they differ from each other in their angular momentum and their magnetic properties. The orbitals that allow one wavelength have a principal quantum number of 2 (n = 2), the orbitals that allow one and a half wavelengths have a principal quantum number of 3 (n = 3), and so on. The set of orbitals with the same principal quantum number make up a shell.

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Physicists use a second number to describe the angular momentum of an orbital. This number is called the orbital’s secondary quantum number, or its angular momentum quantum number (abbreviated l). The number of possible values an orbital can have for its angular momentum is one less than the number of half-wavelengths it allows. This means that an orbital with a principal quantum number of n can have n-1 possible values for its secondary quantum number.

Physicists customarily use letters to indicate orbitals with certain secondary quantum numbers. In order of increasing angular momentum, the orbitals with the six lowest secondary quantum numbers are indicated by the letters s, p, d, f, g, and h. The letter s corresponds to the secondary quantum number 0, the letter p corresponds to the secondary quantum number 1, and so on. In general, the angular momentum of an orbital depends on its shape. An s-orbital, with a secondary quantum number of 0, is spherical. A p-orbital, with a secondary quantum number of 1, resembles two hemispheres, facing one another. The possible combinations of principal and secondary quantum numbers for the first five shells are listed below.

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Subshells

More than one orbital can allow the same number of half-wavelengths and have the same angular momentum. Physicists call orbitals in a shell that all have the same angular momentum a subshell. They designate a subshell with the subshell’s principal and secondary quantum numbers. For example, the 1s subshell is the group of orbitals in the first shell with an angular momentum described by the letter s. The 2p subshell is the group of orbitals in the second shell with an angular momentum described by the letter p.

Orbitals within a subshell differ from each other in their magnetic properties. The magnetic properties of an orbital depend on its shape and orientation in space. For example, a p-orbital can have three different orientations in space: one situated up and down, one from side to side, and a third from front to back.

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Magnetic Quantum Number and Spin

Physicists describe the magnetic properties of an orbital with a third quantum number called the orbital’s magnetic quantum number (abbreviated m). The magnetic quantum number determines how orbitals with the same size and angular momentum are oriented in space. An orbital’s magnetic quantum number can only have whole number values ranging from the value of the orbital’s secondary quantum number down to the negative value of the secondary quantum number. A p-orbital, for example, has a secondary quantum number of 1 (l = 1), so the magnetic quantum number has three possible values: +1, 0, and -1. This means the p-orbital has three possible orientations in space. An s-orbital has a secondary quantum number of 0 (l = 0), so the magnetic quantum number has only one possibility: 0. This orbital is a sphere, and a sphere can only have one orientation in space. For a d-orbital, the secondary quantum number is 2 (l = 2), so the magnetic quantum number has five possible values: -2, -1, 0, +1, and +2. A d-orbital has four possible orientations in space, as well as a fifth orbital that differs in shape from the other four. Together, the principal, secondary, and magnetic quantum numbers specify a particular orbital in an atom.

Electrons are a type of particle known as a fermion. Austrian-American physicist Wolfgang Pauli discovered that no two fermions can have the exact same quantum numbers. This principle is called the Pauli exclusion principle, which states that two or more identical electrons cannot occupy the same orbital in an atom. Scientists know, however, that each orbital can hold two electrons. Electrons have another property, called spin, that differentiates the two electrons in each orbital. An electron’s spin has two possible values: +y (called spin-up) or -y (called spin-down). These two possible values mean that two electrons can occupy the same orbital, as long as their spins are different. Physicists call spin the fourth quantum number of an electron orbital (abbreviated m_s). Spin, in addition to the other three quantum numbers, uniquely describes a particular electron’s orbital.

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