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# Chapter 23: Quantum Physics

Difficulty Level: At Grade Created by: CK-12

A copper vapor pump laser used in an atomic experiment.

As science began to look at very small sizes down to the scale of an atom, our previous intuition about matter broke down.  Quantum mechanics is the solution to what seemed like inconsistent behavior of atoms and light, that resolves dilemmas over what is a wave and what is a particle.  Lasers create a precise wavelength due to quantum mechanics, and are increasingly found throughout everyday life.  This chapter covers black body radiation and Planck's quantum hypothesis, photons and the photoelectric effect, and wave-particle duality.

Chapter Outline

### Chapter Summary

1. The Planck equation relates the energy E\begin{align*}E\end{align*} of a photon of light to its frequency f\begin{align*}f\end{align*}

E=hf\begin{align*}E=hf\end{align*}

where the constant h=6.626×1034 Js\begin{align*}h=6.626 \times 10^{-34} \ J-s\end{align*} is known as Planck’s constant.

According to the photoelectric effect, the maximum kinetic energy KEmax\begin{align*}KE_{max}\end{align*} of the electrons ejected from a material is

KEmax=hfWo\begin{align*}KE_{max}=hf-W_o\end{align*}

where f\begin{align*}f\end{align*} is the frequency of the light incident upon the material and Wo\begin{align*}W_o\end{align*} is the work function of the material : the minimum energy needed to overcome the electrical forces that hold an electron within the material

Wo=hfo\begin{align*}W_o=hf_o\end{align*}

The frequency fo\begin{align*}f_o\end{align*} corresponds to the minimum (threshold) frequency of light necessary to eject a photoelectron.

2. The De Broglie equation for the wavelength of matter waves is

λ=hmv\begin{align*}\lambda = \frac{h}{mv}\end{align*}

where m\begin{align*}m\end{align*} is the mass of a particle, v\begin{align*}v\end{align*} its velocity and λ\begin{align*}\lambda\end{align*} its associated wavelength.

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Jan 13, 2016