Although no currently known elements contain electrons in g...

Although no currently known elements contain electrons in $g$ orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in $g$ orbitals. For $g$ orbitals, the value of $\ell$ is $4 .$ What is the lowest value of $n$ for which $g$ orbitals could exist? What are the possible values of $m_{\ell}$ ? How many electrons could a set of $g$ orbitals hold?

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Key Concepts

Electron Capacity in a Subshell

Each orbital defined by a unique set of quantum numbers can accommodate up to two electrons, each with opposite spins. Given that a subshell with a particular l value contains 2l+1 orbitals, the total electron capacity of a subshell is 2(2l+1). For g orbitals, since l = 4, there are 2(2×4+1) = 2×9 = 18 electrons that can be accommodated.

Magnetic Quantum Number

The magnetic quantum number, m?, specifies the orientation of an orbital in space relative to an external magnetic field. It can take on integer values ranging from -l to +l. Therefore, for g orbitals (l = 4), the possible values for m? are -4, -3, -2, -1, 0, 1, 2, 3, and 4.

Principal Quantum Number

The principal quantum number, n, determines the energy level or shell in which an electron resides. A key rule is that for any orbital with a given angular momentum quantum number (l), n must be at least l+1. This means that for orbitals where l is 4 (g orbitals), the lowest possible n value is 5.

Angular Momentum Quantum Number

The angular momentum quantum number, l, determines the shape and type of an orbital (e.g., s, p, d, f, g, etc.). It can take on integer values from 0 up to n-1. For g orbitals, l is defined as 4, which informs us about the orbital’s complexity and its associated properties.

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