Physical Chemistry , 1st ed.

time. Energy multiplied by time yields a quantity known as action. Earlier in

history, scientists developed something called the principle of least action,

which is an important concept in classical mechanics. In quantum mechanics,

we will find that any quantity that has units of action is intimately related to

Planck’s constant.

Planck’s quantum theory answered one of the great unknowns of earlier sci-

ence, that of blackbody radiation. There were still several unanswered ques-

tions, but quantum theory was the first breakthrough and is typically regarded

as the boundary between classical and modern physics. Any development be-

fore 1900 is considered classical science; after 1900, modern. It was after 1900

that a new understanding of atoms and molecules—the basis of all chem-

istry—was formulated.

9.9 Bohr’s Theory of the Hydrogen Atom

The next step toward an understanding of electrons in atoms was announced

by Danish scientist Niels Henrik David Bohr (Figure 9.18) in 1913 in consid-

ering Rydberg’s general formula, equation 9.17, for the emission lines of the

hydrogen atom spectrum. However, Bohr was considering the Rydberg equa-

tion in light of two new ideas about nature: the nuclear theory of the atom, re-

cently proposed by Rutherford, and the idea of the quantization of a measur-

able quantity,the energy of a photon. (Bohr and Einstein are generally

considered the two most influential scientists of the twentieth century. Which

is more influential is an ongoing debate.)

The nuclear theory of the atom assumed that the negatively charged elec-

tron was in orbit about a more massive nucleus. However, Maxwell’s theory of

electromagnetism requires that when charged matter changes its direction, it

must emit radiation as it accelerates. But electrons in atoms don’t emit radia-

tion as they orbit the nucleus, as far as scientists could tell.

Bohr reasoned that perhaps energy was not the only quantity that could be

quantized. If a particle were traveling in a circular orbit about a nucleus,sup-

pose its angular momentum were quantized?

Bohr made certain assumptions, statements that were not to be justified

but assumedas true, and from these statements he derived certain mathemat-

ical expressions about the electron in the hydrogen atom. His assumptions

were:

1. In the hydrogen atom, the electron moves in a circular orbit about the
   nucleus. Mechanically, the centripetal force that curves the path of the
   electron is provided by the coulombic force of attraction between the op-
   positely charged particles (the negatively charged electron and the posi-
   tively charged proton in the nucleus).


2. The energy of the electron remains constant as the electron remains in
   its orbit about the nucleus. This statement was considered a violation of
   Maxwell’s theory of electromagnetism regarding accelerating charges.
   Since it seems apparent that this “violation” does occur, Bohr suggested
   accepting that it is so.


3. Only certain orbits are allowed, each orbit having a quantized value of
   its angular momentum.


4. Transitions between orbits are allowed, but only when an electron ab-
   sorbs or emits a photon whose energy is exactly equal to the difference
   between the energy of the orbits.

262 CHAPTER 9 Pre-Quantum Mechanics

Figure 9.18 Niels Henrik David Bohr (1885–

1962). Bohr’s work was vital in the development

of modern science. Bohr made the leap from

quantized energy to the quantization of other

measurables; specifically, angular momentum of

subatomic particles like electrons. Bohr and

Einstein argued over many interpretations of the

new theories, but Bohr won most of the argu-

ments. Bohr almost died being smuggled out of

Europe during World War II. He survived to as-

sist in the development of the atomic bomb.

Niels Bohr Archive, courtesy AIP Emilio Segre Visual Archives