Physical Chemistry , 1st ed.

body radiation, but none were any more successful than the Rayleigh-Jeans

law. The matter remained unsolved until 1900. All of the above unexplained

phenomena remained unexplained by the accepted theories of the time. It

wasn’t that these theories were wrong. After hundreds of years of applying the

scientific method, scientists were developing confidence that they were begin-

ning to understand the way the universe acted. These theories were, though,

incomplete. Experiments of the last 40 years of the 1800s began probing parts

of the universe never before seen—the atomic universe—that could not be ex-

plained by the ideas of the time. New ideas, new theories, new ways of think-

ing about the universe were required.

9.8 Quantum Theory

The first step to a better understanding of the universe came in 1900 when the

German physicist Max Karl Ernst Ludwig Planck (Figure 9.14) proposed a rel-

atively simple equation to predict the intensities of blackbody radiation. There

is some speculation that Planck came up with an equation that fit the data and

then reasoned out a justification, rather than supposing a new idea and work-

ing it up to see what would happen. No matter. For our purposes, all that is

important is that he was correct.

Planck was a thermodynamicist, and having studied under Kirchhoff (of

spectroscope fame) in Berlin, he was aware of the blackbody problem and ap-

proached it from a thermodynamic point of view. The exact derivation is not

difficult but is omitted here; texts on statistical thermodynamics include it as

a matter of course. Planck treated light as interacting with electric oscillations

in matter. He supposed that the energy of these oscillations was not arbitrary,

but proportional to their frequency :

Eh (9.21)

where his the proportionality constant. Planck called this amount of energy a

quantum,and we consider that the energy of the oscillator is quantized.He

9.8 Quantum Theory 257

6000 K

R-J law

Blackbody radiation

4  106

0

0

Wavelength (m)

400

Intensity (arbitrary units)

50 100 150 200 250 300 350

3  106

2  106

1  106

Figure 9.13 Early attempts at modeling the behavior of a blackbody included the Rayleigh-

Jeans law. But as this plot illustrates, at one end of the spectrum the calculated intensity grows

upward to infinity, the so-called ultraviolet catastrophe.

Figure 9.14 Max Karl Ernst Ludwig Planck

(1858–1947). Planck’s quantum theory, proposed

in 1900, marks the beginning of modern science.

Trained as a thermodynamicist, he based his the-

ory on thermodynamic arguments. It is said that

he had some misgivings about the truth of his

own ideas until experimental evidence was found

in support of them. The Kaiser Wilhelm Society

was renamed the Max Planck Institute in his

honor in 1930 and is still a major institution in

Germany. He received the Nobel Prize in 1918.

© CORBIS-Bettmann