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  • Explain Max Planck’s contribution to the development of quantum mechanics.
  • Explain why atomic spectra indicate quantization.

Planck’s contribution

Energy is quantized in some systems, meaning that the system can have only certain energies and not a continuum of energies, unlike the classical case. This would be like having only certain speeds at which a car can travel because its kinetic energy can have only certain values. We also find that some forms of energy transfer take place with discrete lumps of energy. While most of us are familiar with the quantization of matter into lumps called atoms, molecules, and the like, we are less aware that energy, too, can be quantized. Some of the earliest clues about the necessity of quantum mechanics over classical physics came from the quantization of energy.

The blackbody radiation graph of E M radiation intensity versus wavelengths is shown, with the visible band represented as vertical colored strip marked on x axis. Wavelength is along x axis and E M radiation intensity is along y axis. The variation of E M radiation intensity is shown by three curves that start at origin, rise up to their highest point and then drop toward the x axis smoothly, and finally extend parallel to the x axis. There are three curves for three different temperatures, and each has a different peak for radiation intensity. As the temperature decreases, the peak of the black body radiation curves moves to a lower radiation intensity and longer wavelength.
Graphs of blackbody radiation (from an ideal radiator) at three different radiator temperatures. The intensity or rate of radiation emission increases dramatically with temperature, and the peak of the spectrum shifts toward the visible and ultraviolet parts of the spectrum. The shape of the spectrum cannot be described with classical physics.

Where is the quantization of energy observed? Let us begin by considering the emission and absorption of electromagnetic (EM) radiation. The EM spectrum radiated by a hot solid is linked directly to the solid’s temperature. (See [link] .) An ideal radiator is one that has an emissivity of 1 at all wavelengths and, thus, is jet black. Ideal radiators are therefore called blackbodies , and their EM radiation is called blackbody radiation    . It was discussed that the total intensity of the radiation varies as T 4 , size 12{T rSup { size 8{4} } } {} the fourth power of the absolute temperature of the body, and that the peak of the spectrum shifts to shorter wavelengths at higher temperatures. All of this seems quite continuous, but it was the curve of the spectrum of intensity versus wavelength that gave a clue that the energies of the atoms in the solid are quantized. In fact, providing a theoretical explanation for the experimentally measured shape of the spectrum was a mystery at the turn of the century. When this “ultraviolet catastrophe” was eventually solved, the answers led to new technologies such as computers and the sophisticated imaging techniques described in earlier chapters. Once again, physics as an enabling science changed the way we live.

The German physicist Max Planck (1858–1947) used the idea that atoms and molecules in a body act like oscillators to absorb and emit radiation. The energies of the oscillating atoms and molecules had to be quantized to correctly describe the shape of the blackbody spectrum. Planck deduced that the energy of an oscillator having a frequency f size 12{f} {} is given by

E = n + 1 2 hf . size 12{E= left (n+ { { size 8{1} } over { size 8{2} } } right ) ital "hf"} {}

Here n size 12{n} {} is any nonnegative integer (0, 1, 2, 3, …). The symbol h size 12{h} {} stands for Planck’s constant    , given by

h = 6 . 626 × 10 –34 J s . size 12{h = 6 "." "626" times " 10" rSup { size 8{"–34"} } " J " cdot " s"} {}

The equation E = n + 1 2 hf size 12{E= left (n+ { { size 8{1} } over { size 8{2} } } right ) ital "hf"} {} means that an oscillator having a frequency f size 12{f} {} (emitting and absorbing EM radiation of frequency f size 12{f} {} ) can have its energy increase or decrease only in discrete steps of size

Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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