Question

Which quantum number defines a shell? Which quantum numbers define a subshell?

Short answer

The principal quantum number defines a shell while the angular momentum and magnetic quantum numbers define a subshell.

Step-by-step solution

Quantum Numbers Definition

Firstly, it must be understood what quantum numbers are. Quantum numbers are a set of four numbers used to describe the unique state of an electron in an atom. The four quantum numbers include the principle quantum number (\(n\)), angular momentum quantum number (\(l\)), magnetic quantum number (\(m_l\)), and spin quantum number (\(s\)).

Identify the Shell-defining Quantum Number

Having known their general roles, let's now identify which quantum number represents a shell. The principal quantum number (\(n\)) is the quantum number that defines the shell of an atom. It describes the energy level and size of the orbital. The value of \(n\) can take on any positive integer, and the value increases with distance from the nucleus of the atom.

Identify the Subshell-defining Quantum Numbers

To identify which quantum numbers represent a subshell, we need to understand that both the angular momentum quantum number (\(l\)) and the magnetic quantum number (\(m_l\)) define the subshells of an atom. The value of \(l\) determines the shape of the orbital (subshell) and ranges from 0 to \(n-1\). The magnetic quantum number (\(m_l\)) further defines the spatial orientation of the subshell and ranges from \(-l\) to \(+l\).