Chapter 6, Problem 58QP

Interpretation Introduction

Interpretation:

The possible values of $l$ and $m_l$ for $n=3$ are to be determined.

Concept introduction:

The four quantum numbers are the principle quantum number (n), the angular quantum number (l), the magnetic spin quantum number $\left(m_l\right)$, and the electron spin quantum number $\left(m_s\right)$.

The principle quantum number designates the orbital size. The angular momentum quantum number tells the shape of the atomic orbital. The possible range of l is from $0$ to $n-1$. The magnetic quantum number tells the orientation of the atomic orbital in space. The possible range of $m_l$ is from $-l\text{ to}+l$. The electron spin quantum number tells the electron spin in an orbital in space. The possible spins are $+\frac{1}{2}\text{ or }-\frac{1}{2}$.