Question

What is the lowest value of \(n\) that allows \(g\) orbital to exist? (a) 6 (b) 7 (c) 4 (d) 5

Short answer

The lowest value of n that allows a g orbital to exist is 5.

Step-by-step solution

Identify the Orbital

A g-type orbital is part of the series of orbitals that are defined by the azimuthal quantum number, l. The value of l for an s-orbital is 0, for p-orbital is 1, for d-orbital is 2, and for f-orbital is 3 and so on. Each type of orbital is defined by the letter that is one position further in the alphabet. Thus, a g-orbital corresponds to the azimuthal quantum number l = 4.

Determine the Principal Quantum Number

The principal quantum number, n, must always be greater than the azimuthal quantum number l since n determines the energy level of the electron. The lowest possible value for n that allows for a g-orbital is when n = l + 1.

Calculate the Lowest Value of n

Since the azimuthal quantum number for the g-orbital is l = 4, the lowest possible value for the principal quantum number n that allows for a g-orbital is n = l + 1 = 4 + 1 = 5.

Key concepts

Quantum Numbers

Quantum numbers are essential for understanding the complex arrangement of electrons within an atom. They serve as unique identifiers for the energy levels, shapes, orientations, and spins of an atom's electrons. There are four types of quantum numbers: principal (n), azimuthal (l), magnetic (m_l), and spin (s). They collectively describe the exact 'address' of an electron within an atom, providing a clear set of instructions for locating it. Think of them as the electrons' home address within the vast city of an atom.

Each quantum number limits the value of the next. For example, the principal quantum number determines the energy level and the likely distance of an electron from the nucleus, while the azimuthal quantum number divides these energy levels into sublevels and dictates the shape of the region an electron can be found.

Azimuthal Quantum Number

The azimuthal quantum number, denoted as 'l', is responsible for determining the shape of an electron's orbital. It is intimately connected to the angular momentum of the electron within that orbital. With values ranging from 0 to n-1, where 'n' is the principal quantum number, 'l' defines the type of orbital: s (sharp), p (principal), d (diffuse), and f (fundamental). To cover the shapes that follow f orbitals, we extend the sequence alphabetically, albeit skipping 'j'. This means that the next possible shapes are g, h, and so on.

In this context, for a g-orbital, 'l' is equal to 4. The pattern indicates each alphabet letter corresponds to an increasing integer value of 'l', starting from 0 for s-orbitals. It provides a step towards grasping the complexity of electron configurations in higher energy levels, reflecting the vast array of possible atomic behaviors.

Principal Quantum Number

The principal quantum number, designated as 'n', represents the energy level of an electron in an atom. It defines the possible distance ranges of an electron from the nucleus, contributing to the size of the orbital. 'n' can possess any positive integer value starting from 1 upwards, with each step up the 'n' ladder moving an electron to an energy level further from the nucleus that contains more sub-levels.

Since energy levels and azimuthal sub-levels are intrinsically linked, 'n' must always be greater than 'l' for a valid electron configuration to exist. Accordingly, the requirement for a g-orbital to exist—the question at hand—means finding the minimum 'n' that's bigger than 4, the azimuthal quantum number for g-orbitals.

Orbital Types

Orbitals are regions within an atom where electrons are most likely to be found. They come in various shapes and sizes, denoted by the letters s, p, d, f, and onwards. Each orbital type corresponds to a specific range of the azimuthal quantum number (l). For instance, an s-orbital has l = 0, a p-orbital has l = 1, while d and f orbitals correspond to l = 2 and l = 3, respectively. Moving past the commonly known orbitals, we encounter the g-orbital starting at l = 4.

The type of orbital defines not just the shape, but also the number of electrons it can hold. It is critical to the assembly of the periodic table and the prediction of chemical properties of atoms. For instance, g-orbitals, though yet to be observed occupied in naturally occurring elements, can theoretically hold up to 18 electrons, and their existence broadens our understanding of potential chemical behaviors in superheavy, yet-to-be-discovered elements.