Name: electron regions in atomic orbitals
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 44 s
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Atomic Orbitals

The densest region of the electron cloud &#8212; where an electron is most likely to be found &#8212; is described in terms of atomic orbitals. 

The shape of an atomic orbital is determined by the angular momentum quantum number, l. Recall that the values of l are based on the principal quantum number, n &#8212; possible values of l range from 0 to n &#8722; 1. When n is greater than one, multiple sublevels exist. Each value of l corresponds to either an s, p, d, or f orbital.

The lowest energy orbital is the 1s orbital. This is a spherically symmetric orbital. The probability density of a 1s orbital reveals that the electron is most likely to be found at the nucleus. However, given the electrostatic forces between protons and electrons &#8212; this isn&#8217;t likely. 

Multiplying the probability density by the volume of thin spherical shells with radii r is more representative. The total probability of finding an electron within the thin shell at a distance r from the nucleus is the radial distribution function. 

For hydrogen, the greatest probability of finding an electron is at 52.9 picometers from the nucleus. Thus, the shape of the 1s atomic orbital for hydrogen is spherical with a radius of 52.9 picometers.

The 2s and 3s orbitals are also spherical. They are larger and have nodes. At a node, the probability of finding an electron is zero. 

Principal levels with n equal to two or more also contain three p-orbitals. These are lobe-shaped with a node at the nucleus. Their orientation is described by the value of ml. The three p-orbitals are orthogonal to each other.

Principal levels of n equal to three or more also have five d orbitals. The d orbitals with the cloverleaf shape have four electron-dense lobes and two perpendicular nodal planes. One of the d-orbitals is slightly different. 

The f orbitals have more lobes and nodes. These orbitals exist for principal levels of n equal to four or more. 

When you overlay the orbitals on top of one another, a roughly spherical shape emerges. This is why atoms are generally represented as spheres.

atomic orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud. 

The angular momentum quantum number is an integer that may take the values, l = 0, 1, 2, &#8230;, n &#8211; 1. An orbital with a principal quantum number of 1 (n = 1) can have only one value of l (l = 0), whereas a principal quantum number of 2 (n = 2) permits l = 0 and l = 1. Orbitals with the same value of l define a subshell.

Orbitals with l = 0 are called s orbitals and they make up the s subshells. The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (i.e., 3p if n = 3). The orbitals with l = 2 are called the d orbitals. The orbitals with l = 3, 4, and 5 are the f, g, and h orbitals. 

The lowest energy orbital is the 1s orbital. This is a spherically symmetric orbital. The probability density (&#968;2) of a 1s orbital implies that the electron is most likely to be found at the nucleus. However, given the electrostatic forces between protons and electrons, this does not accurately represent where the electron will reside. Instead, the Radial Distribution Function is used, which is a plot of the total probability of finding an electron in an orbital at a given radius r. The radial distribution function is found by multiplying the probability density by the volume of thin spherical shells with radii, r. For the 1s orbital of hydrogen, the Radial Distribution Function has a value zero at the nucleus, which increases to a maximum at 52.9 picometers before decreasing with increasing r.

There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction &#968; is zero at this distance for this orbital. Such a value of r is called a radial node. The number of radial nodes in an orbital is n &#8211; l &#8211; 1. For 2s orbitals, where n = 1, there is one radial node, whereas 3s orbitals have two radial nodes. 

Each principal level with n = 2 or more contains three p orbitals. The three p orbitals have two lobes with a node located at the nucleus . The orientation of p orbitals in space is described by the value of ml. The three p orbitals are mutually perpendicular (orthogonal) to each other. The higher p orbitals (3p, 4p, 5p, and higher) have similar shapes but are larger in size with additional radial nodes.

Principal levels with n = 3 or more contain five d orbitals. Four of these orbitals consist of a cloverleaf shape, with four electron-dense lobes. There are two perpendicular nodal planes that intersect at the nucleus. At these nodal planes, the electron density is zero. One of the d orbitals is slightly different in shape and has two lobes oriented in the z-axis with a donut-shaped ring in the xy plane. Principal levels with n = 4 and greater contain seven f orbitals, which have complex shapes. These orbitals have more nodes and lobes than d orbitals.

<img alt="Atomic orbital diagram showing s, p, d, and f orbitals with 3D coordinate axes for electron distribution." src="/files/core/CDNSource/lessons/983/983Image%201.png" style="width: 700px;" data-altupdatedat="1754904545000" data-alt="Atomic orbitals diagram: s, p, d, f orbitals shapes in 3D, illustrating electron distribution." />

Figure 1: Representative s, p, d, and f orbitals.

These different shapes of the atomic orbitals represent the three-dimensional regions within which the electron is likely to be found. All the orbitals together make up a roughly spherical shape, which is why atoms are generally represented as spheres.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/6-3-development-of-quantum-theory">Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory.</a>

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

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electron regions in atomic orbitals

Electron regions in atomic orbitals show where an electron is most likely to be found in an atom. These three-dimensional regions are often drawn as boundary surfaces around the densest part of the cloud.

The shape of an orbital depends on the angular momentum quantum number, l. This value can range from 0 to n - 1, where n is the principal quantum number. For n = 1, only l = 0 is allowed. For n = 2, both l = 0 and l = 1 are allowed.

Orbitals with the same value of l form a subshell. The l = 0 orbitals are s orbitals, and they make up s subshells. The l = 1 orbitals are p orbitals, which form a p subshell such as 3p when n = 3. The l = 2 orbitals are d orbitals. The l = 3, 4, and 5 orbitals are called f, g, and h orbitals.

The lowest-energy orbital is the 1s orbital. It is spherically symmetric. The probability density, ψ², suggests that an electron is most likely found at the nucleus. But this does not fully match electron behavior. The radial distribution function gives the total probability of finding an electron at a distance r from the nucleus. It is found by multiplying the probability density by the volume of thin spherical shells.

For the 1s orbital of hydrogen, the radial distribution function is zero at the nucleus. It rises to a maximum at 52.9 picometers and then decreases as r increases. Some distances from the nucleus have zero probability density for a given orbital. These points are called radial nodes. The number of radial nodes is n - l - 1. A 2s orbital has one radial node, and a 3s orbital has two.

Each principal level with n = 2 or more contains three p orbitals. Each p orbital has two lobes and a node at the nucleus. Their orientation in space is described by m_l. The three p orbitals are mutually perpendicular. Higher p orbitals, such as 3p, 4p, and 5p, have the same general shape but are larger and contain additional radial nodes.

Principal levels with n = 3 or more contain five d orbitals. Four of them have a cloverleaf shape with four electron-dense lobes. They also have two perpendicular nodal planes that meet at the nucleus. The fifth d orbital has two lobes along the z-axis and a donut-shaped ring in the xy plane.

Principal levels with n = 4 and greater contain seven f orbitals. These orbitals have complex shapes with more nodes and lobes than d orbitals. Together, s, p, d, and f orbitals help explain why atoms are often drawn as spheres, even though the electron regions inside them have distinct shapes.

Electron Regions in Atomic Orbitals

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Explore electron regions in atomic orbitals, including s, p, d, and f shapes, radial nodes, and the radial distribution function for high school chemistry.

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Electron Regions in Atomic Orbitals

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