Page 165 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

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The hydrogen atom

A theoretical understanding of the structure and behavior of the hydrogen atom
is essential to the ®elds of physics and chemistry. As the simplest atomic
system, hydrogen must be understood before one can proceed to the treatment
of more complex atoms, molecules, and atomic and molecular aggregates. The
È
hydrogen atom is one of the few examples for which the Schrodinger equation
can be solved exactly to obtain its wave functions and energy levels. The
resulting agreement between theoretically derived and experimental quantities
serves as con®rmation of the applicability of quantum mechanics to a real
chemical system. Further, the results of the quantum-mechanical treatment of
atomic hydrogen are often used as the basis for approximate treatments of more
È
complex atoms and molecules, for which the Schrodinger equation cannot be
solved.
The study of the hydrogen atom also played an important role in the
development of quantum theory. The Lyman, Balmer, and Paschen series of
spectral lines observed in incandescent atomic hydrogen were found to obey
the empirical equation

1 1
í ˆ Rc ÿ , n 2 . n 1
n 2 n 2
1 2
where í is the frequency of a spectral line, c is the speed of light, n 1 ˆ 1, 2, 3
for the Lyman, Balmer, and Paschen series, respectively, n 2 is an integer
determining the various lines in a given series, and R is the so-called Rydberg
constant, which has the same value for each of the series. Neither the existence
of these spectral lines nor the formula which describes them could be explained
by classical theory. In 1913, N. Bohr postulated that the electron in a hydrogen
atom revolves about the nucleus in a circular orbit with an angular momentum
that is quantized. He then applied Newtonian mechanics to the electronic
motion and obtained quantized energy levels and quantized orbital radii. From

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