Chapter 6, Problem 56QP

Interpretation Introduction

Interpretation:

The four quantum numbers that determine the energy of an electron in an atom, the size of an orbital, the shape of an orbital, and the orientation of an orbital in space are to be predicted.

Concept introduction:

The four quantum numbers are principle quantum number $\left(n\right)$, angular quantum number $\left(l\right)$, magnetic spin quantum number $\left(m_l\right)$, and 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 $+\frac{1}{2}\text{ or }-\frac{1}{2}$.