Quantization is the process of changing a continuous variable into a variable that has only discrete values. Energy, in classical physics, can have any value. But things are different at the atomic level.

• The energy of a light wave is divided into discrete “chunks,” or quanta, called photons.

• The electrons of an atom can exist only in certain states with discrete energies. These are the quantum states of the atom.

The photon model of light says that light consists of particle-like units called photons.

• The energy of a photon of frequency $f$ is quantized: $E_{\text{photon}}=hf$, where $h$ is Planck’s constant.

• At very low intensity, light is detected as discrete particle-like events.

《 LOOKING BACK Section 33.2 Interference

• Photons explain the photoelectric effect, where short-wavelength light ejects electrons from a metal surface but long-wavelength light does not.

• Photons also explain Compton scattering, where the wavelength of x rays is shifted when the x rays scatter from a target.

  

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You’ll learn that particles of matter, such as electrons and neutrons, have wave-like properties and can even undergo interference. The de Broglie wavelength of a particle of mass $m$ and speed $v$ is $\lambda =h/mv$, where, again, $h$ is Planck’s constant.

• A wave-like particle confined to a box sets up standing waves as it reflects back and forth. You’ll see that this leads to quantized energy levels.

• The quantum theory of matter, beginning with Bohr and continuing with quantum mechanics (see Chapter 40) is based on matter’s wave-like properties.

  

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The Bohr model adds quantum ideas to Rutherford’s solar-system atom.

• Electrons can orbit with only certain discrete radii and energies.

• Photons are emitted and absorbed when electrons jump between energy levels.

《 LOOKING BACK Section 37.6 Rutherford’s model