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# Chapter 24: Atomic Physics

Difficulty Level: At Grade Created by: CK-12

Credit: Beltsville Agricultural Research Center
Source: http://commons.wikimedia.org/wiki/File:Snow_crystals.png
License: CC BY-NC 3.0

A scanning electron microscope image of snow crystals, with computer-generated colors. [Figure1]

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 Outline

### Chapter Summary

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

1λ=R(1221n2),n=3,4,\begin{align*}\frac{1}{\lambda}=R\left(\frac{1}{2^2}-\frac{1}{n^2}\right), n=3,4, \ldots\end{align*},

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

R=1.097×107 m1\begin{align*}R=1.097 \times 10^7 \ m^{-1}\end{align*}

The integer n\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

1λ=R(1n2l1n2h)\begin{align*}\frac{1}{\lambda}=R \left(\frac{1}{n^2_l}-\frac{1}{n^2_h}\right)\end{align*}

where nl\begin{align*}n_l\end{align*} is the lower state and nh\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

rn=n2r1,n=1,2,\begin{align*}r_n=n^2 r_1, n=1, 2, \ldots\end{align*}

where r1\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

E=E1n2,n=1,2,\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

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

where Eh\begin{align*}E_h\end{align*} is a higher energy state of the electron and El\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

ΔxΔph2π\begin{align*}\Delta x \Delta p \ge \frac{h}{2 \pi}\end{align*}

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

1. [1]^ Credit: Beltsville Agricultural Research Center; Source: http://commons.wikimedia.org/wiki/File:Snow_crystals.png; License: CC BY-NC 3.0

Dec 05, 2014