Environmental Engineering Reference
In-Depth Information
3
Atoms, Molecules, and Semiconductor Devices
We found in Chapter 2 that the release of energy from the sun starts when protons
come together to form deuterons, a process that would not happen in classical
physics. The wave property of particles of matter, as developed in the Schrodinger
equation, was needed, also, to explain the alpha decay of uranium and thorium
nuclei. We now extend Schrodingers method to more familiar matter, in the form of
atoms, molecules, and semiconductors. The solar cell, which produces electrical
energy from sunlight, in fact, requires a sophisticated understanding of the semi-
conductor PN junction. So, we need to become expert in the application of
Schrodingers equation introduced in Chapter 2 to the cases of interest, including
photovoltaic solar cells.
3.1
Bohr
s Model of the Hydrogen Atom
To begin, we describe a useful simple model of the atom, essentially an electron
orbiting around a proton. Bohr made a semiclassical model of the atom that
rst
explained the sharply de
ned energy levels, a puzzling feature not present in any
classical model of atoms. These levels were suggested by the optical spectra, which
were composed of sharp lines. Even though this model is incorrect in some
respects, it easily leads to exact results for the orbit radius, energy levels, and the
wavelengths of light absorption and emission of the one electron atom. It is well
worth learning.
Bohrs model describes a single electron orbiting a massive nucleus of charge
þZe
. Bohr knew that the nucleus of the atomwas a tiny object, much smaller in size
than the atom itself, containing positive charge
Ze
, with
Z
the atomic number and
e
the electron charge, 1.6
10
19
C. The proton
m
p
¼
1.67
10
27
kg is much more
massive than the electron,
m
e
¼
9.1
10
31
kg, thus
M
/
m¼
1835, so that nuclear
motion can often be neglected. In the motion of two particles about a common center
of mass, the relative motion can be corrected for the small motion of the heavier
particle
M
by using the reduced mass
m
r
¼mM
/(
m þ M
)so
m
r
m
e
(1
m
e
/
m
p
)
¼m
e
attractive Coulomb force
F¼ k
c
Ze
2
/
r
2
, where
(1
1/1835). The
