# Chapter 24: Atomic Physics

**At Grade**Created by: CK-12

A scanning electron microscope image of snow crystals, with computer-generated colors.

A scanning electron microscope is a tool that uses electrons to make very sharp images with magnification of up to 500,000x. Our knowledge of electrons comes from early study of the atom that lead to greater understanding not only of electrons and atomic structuer, but of the nature of all particles. This chapter covers modeling the atom and atomic spectra, the Bohr atom, and the Uncertainty Principle.

### Chapter Summary

1. The Balmer series is an empirical formula which gives the reciprocal of the wavelength \begin{align*}\lambda\end{align*} for each line in the hydrogen spectrum

\begin{align*}\frac{1}{\lambda}=R\left(\frac{1}{2^2}-\frac{1}{n^2}\right), n=3,4, \ldots\end{align*},

The letter \begin{align*}R\end{align*} is known as the Rydberg constant of value

\begin{align*}R=1.097 \times 10^7 \ m^{-1}\end{align*}

The integer \begin{align*}n\end{align*} is associated with each emission line.

2. Bohr quantized assumptions led to a more general statement of the Balmer series

\begin{align*}\frac{1}{\lambda}=R \left(\frac{1}{n^2_l}-\frac{1}{n^2_h}\right)\end{align*}

where \begin{align*}n_l\end{align*} is the lower state and \begin{align*}n_h\end{align*} is the higher state.

3. Bohr’s assumptions for hydrogen atom are:

a. The allowed radii of the atom

\begin{align*}r_n=n^2 r_1, n=1, 2, \ldots\end{align*}

where \begin{align*}r_1\end{align*} is the smallest orbital radius of the hydrogen atom, commonly referred to as the *Bohr radius*.

b. The allowable energy levels, or stationary states of the atom

\begin{align*}E=\frac{E_1}{n^2}, n=1, 2, \ldots\end{align*}

c. The difference between allowable energy levels can be expressed as

\begin{align*}hf=E_h-E_l\end{align*}

where \begin{align*}E_h\end{align*} is a higher energy state of the electron and \begin{align*}E_l\end{align*} is a lower energy state of the electron.

4. The square of the amplitude of the matter wave in Schrodinger’s equation assigns probabilities for the location of the electron.

5. The Heisenberg uncertainty principle is

\begin{align*}\Delta x \Delta p \ge \frac{h}{2 \pi}\end{align*}

where \begin{align*}\Delta x\end{align*} is the uncertainty in position of the particle and \begin{align*}\Delta p\end{align*} is the uncertainty in momentum of the particle.

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