Page 224 - Essentials of physical chemistry

186 Essentials of Physical Chemistry

FIGURE 9.4 Niels Henrik David Bohr (1885–1962) was a Danish physicist who unified spectral data from
atoms (mainly H) with a theory of quantized energy in 1913 for which he was awarded the Nobel Prize in
Physics in 1922. He earned his doctorate in 1911 from the University of Copenhagen and then studied further
under Ernest Rutherford in Manchester England who was studying the nature of atomic structure. He
hypothesized the multielectron shells which were useful in organizing chemical concepts. Bohr became a
professor of physics at the University of Copenhagen in 1916. In 1920, he was named director of the Institute of
Theoretical Physics at the University of Copenhagen. He was named a Fellow of the Royal Society of London
in 1926 and received the Royal Society Copley Medal in 1938. He fled Denmark during WWII and assisted
scientists in the Manhattan project at Los Alamos in the United States but returned to Copenhagen after the war
and promoted the peaceful uses of atomic energy.

energy as well. While this is reasonable after the fact, it took the genius of Bohr to extend this
to angular momentum as mvr ¼ n h:

mv 2 (mv) 2 p 2
2 2m 2m
E ¼ ¼ ¼
and momentum p ¼ mv.
Thus, if energy is quantized (Planck 1901), momentum is even more fundamental than energy,
because energy can be expressed in terms of momentum. The discovery of quantized energy and the
fact that energy can be expressed in terms of momentum implies that momentum is probably
quantized as well. Then angular momentum in a rotating system should also be quantized and only
exist as specific chunks, according to Bohr’s hypothesis. By 1913, only a few people really believed
that energy is ‘‘chunkified,’’ but the combination of Planck’s blackbody spectrum in 1901 and
Einstein’s 1905 explanation of the photoelectric effect had convinced a few scientists that quant-
ization of both energy and momentum does exist. Whereas Planck had used ‘‘h’’ as his proportion-
h
ality constant for quantized energy, Bohr chose ‘‘ ’’ (h-bar) as the basic unit of angular momentum
h
in a rotating system where h-bar ¼ Planck’s . We are now going to show Bohr’s derivation that is
2p