Chapter 7, Problem 7.7QE

Interpretation Introduction

Interpretation:

The affect of electron spin quantum number on the energy of the electron in a hydrogen atom has to be determined.

Concept Introduction:

Erwin Schrödinger gave a model to describe the behavior of an electron in atoms through a wave function. The wave function is defined as a mathematical function for an electron wave that gives the amplitude of the wave at any point in space. It is represented by a Greek letter $\Psi$.

The acceptable wave function is characterized by a set of four quantum numbers. These quantum numbers are related to the shape, size of the electron wave and the location of the electron in space.

These quantum numbers are represented by $n$, $l$, $m_l$, and $m_s$. The quantum number $n$ is known as the principal quantum number and it allowed values are all positive whole numbers. The quantum number $l$ is known as angular momentum quantum number and its allowed values are all positive integer from zero to $n-1$. The quantum number $m_l$ is known as magnetic quantum number and its allowed values lie between $-l$ to $+l$. The quantum number $m_s$ is known as electron spin quantum number and its allowed values are $+\text{1/2}$ and $-\text{1/2}$.