A Suppose you live in a different universe where a different...

A Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms of that universe. These quantum numbers have the following rules: $N,$ principal $1,2,3, \ldots, \infty$ $I_{7}$ orbital $\quad=N$ $M,$ magnetic -1,0,+1 How many orbitals are there altogether in the first three electron shells?

A Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms of that universe. These quantum numbers have the following rules:
$N,$ principal $1,2,3, \ldots, \infty$
$I_{7}$ orbital $\quad=N$
$M,$ magnetic -1,0,+1
How many orbitals are there altogether in the first three electron shells?

Key Concepts

Electron Shells

Electron shells are layers or groups of orbitals that surround an atom's nucleus, classified by the principal quantum number. Each shell consists of a set of orbitals determined by rules involving other quantum numbers, such as the orbital and magnetic quantum numbers. The overall arrangement and number of orbitals per shell form the basis of an atom's electronic structure.

Magnetic Quantum Number

The magnetic quantum number specifies the orientation of an orbital in space relative to an external magnetic field. It is determined by the orbital angular momentum and typically takes on a set of discrete values, which leads to orbital degeneracy – that is, several orbitals having the same energy but different spatial orientations. This concept is fundamental in understanding the multiplicity of orbitals within each subset defined by other quantum numbers.

Orbital Quantum Number

This quantum number, typically representing angular momentum, defines the shape of an orbital. In many quantum systems, it can range from 0 up to n-1 for a given principal quantum number; however, in variant systems, it might be set equal to the principal quantum number or follow an alternate rule. Its importance lies in distinguishing between different orbital types within a given energy level.

Principal Quantum Number

This quantum number, often denoted as n, identifies the electron shell or energy level in which an electron is found. It determines the overall size and energy of an orbital and takes on positive integer values starting from 1. In different contexts or universes, the definition of higher quantum numbers may vary, but its role in setting the stage for the structure of electron shells remains crucial.

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