or packets of energy. The energy of a beam of a particular color of light must be a multiple of the energy of the packets that make it up. This
realization had profound implications for the understanding of both light itself and the atoms that emit the light.
36.2 - Balmer series
“The most important result of the application of
quantum mechanics to the description of electrons in
a solid is that the allowed energy levels of electrons
will be grouped into bands.” So wrote Andy Grove,
then an employee of the Intel Corporation and a
faculty member of the University of California at
Berkeley, in his text on the physics and technology of
semiconductor devices. Grove became the chairman
of Intel during its rise to power, prestige and
profitability.
Grove cites two quantum principles. First, the concept
that there are “energy levels” for electrons, and
second, that these are grouped into bands (the
emphasis in the quote is his).
For now, we will simplify our discussion by focusing on energy levels. Bands refer to the
fact that certain electrons exist at energy levels that are close to one another. In
practical applications, the distinction between a band and an energy level is often
dropped.
Grove’s words convey how important the ideas of quantum theory are for
semiconductor science and technology. We use these words to motivate the next few
sections of this book. One might wonder: How did physicists discover that atomic
electrons had discrete energy levels? In other words, how did they first learn that the
energy levels of electrons are quantized, not continuous?
Physicists advanced the theory as their observations forced them to. The story begins
in 1666 when Newton showed that a prism could disperse sunlight into a spectrum of
colors. Today, one would say Newton showed that sunlight comprises light of many
wavelengths: Light perceived as white is in fact made up of a rainbow of components of
various hues. When it was first discovered, the spectrum of sunlight seemed to be a
continuous gamut of colors.
A series of later experiments convinced scientists that light had a wavelike nature. They
could create interference patterns with light that were conceptually identical to patterns
created by water waves. Physicists even found that they could measure the
wavelengths of various colors of light. One mystery of science seemed to be solved:
Light was a wave.
However, in 1814, the German physicist Joseph von Fraunhofer made careful
observations using a thin slit, and discovered that the spectrum of sunlight contained
many narrow dark lines, or gaps. In other words, certain wavelengths of light were not
present in the spectrum he was observing. He discovered that the spectrum of sunlight
was not continuous.
Throughout the 1800s, scientists studied the light emitted and absorbed by various
gases. They discovered that a gas like hydrogen only emits or absorbs light of specific
wavelengths. By 1880, the wavelengths of the spectral lines of various elements,
including most famously hydrogen, were well known. In Concept 1 you see an
illustration of the spectral lines in the emission spectrum of excited hydrogen gas.
The distinct colors and wavelengths of light you see are characteristic of light emitted by
this element. Similar lines, but with different colors í wavelengths í can be found when
the light of a neon sign, or the glow of a fluorescing ruby, is analyzed. (Each element
has a corresponding absorbtion spectrum, consisting of dark lines at exactly the same
wavelengths, against a rainbow background.)
As you can see, the spectral lines of hydrogen are sharp and distinct, not blurred. For
instance, the red light you see has a wavelength of 656.3 nanometers, the blue-green light has a wavelength of 486.1 nm, and the violet light
has a wavelength of 434.1 nm. Hydrogen atoms emit this light after being “excited” by an electrical discharge through the gas, caused by a
potential difference of 5000 volts applied between two electrodes.
The discrete nature of the hydrogen spectrum puzzled and intrigued physicists. Why did the light emitted by hydrogen only exist at certain
wavelengths, rather than being continuous like a rainbow? And why at these particular wavelengths? Was there any way to predict the
wavelengths?
A Swiss high school teacher, J. J. Balmer, analyzed the pattern. He determined that the wavelengths were not random, but could be
determined using the formula in Equation 1. The constant RH that appears in Balmer’s formula is called the Rydberg constant.
Intriguing mathematical patterns did not stop with the set of spectral lines known as the Balmer series. There are also wavelengths emitted by
The electrically excited neon gas in this sign emits light
at several sharply defined red-orange wavelengths.Hydrogen emission spectrum
Is not continuous