# Chapter 23: Quantum Physics

**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.

- 23.1.
## Blackbody Radiation and Planck’s Quantum Hypothesis

- 23.2.
## Photons and the Photoelectric Effect

- 23.3.
## Wave-Particle Duality

### Chapter Summary

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

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

where the constant \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 \begin{align*}KE_{max}\end{align*} of the electrons ejected from a material is

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

where \begin{align*}f\end{align*} is the frequency of the light incident upon the material and \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

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

The frequency \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

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

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