7.11
The densest region of the electron cloud — where an electron is most likely to be found — 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 — possible values of l range from 0 to n − 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 — this isn’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.
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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