http://www.ck12.org Chapter 5. Electrons in Atoms
FIGURE 5.13
Heisenberg Uncertainty Principle: The
observation of an electron with a micro-
scope requires reflection of a photon off
of the electron. This reflected photon
causes a change in the path of the elec-
tron.Electrons do not travel around the nucleus in simple circular orbits.
The location of the electrons in the quantum mechanical model of the atom is often referred to as an electron cloud.
The electron cloud can be thought of in the following way. Imagine placing a square piece of paper on the floor
with a dot in the circle representing the nucleus. Now take a marker and drop it onto the paper repeatedly, making
small marks at each point the marker hits. If you drop the marker many, many times, the overall pattern of dots
will be roughly circular. If you aim toward the center reasonably well, there will be more dots near the nucleus and
progressively fewer dots as you move away from it. Each dot represents a location where the electroncould beat
any given moment. Because of the uncertainty principle, there is no way to know exactly where the electron is. An
electron cloud has variable densities: a high density where the electron is most likely to be and a low density where
the electron is least likely to be (Figure5.14).
In order to specifically define the shape of the cloud, it is customary to refer to the region of space within which there
is a 90% probability of finding the electron. This is called anorbital, which can be defined asa three-dimensional
region of space in which there is a high probability of finding an electron.
Atomic Orbitals and Quantum Numbers
Solutions to the Schrödinger wave equation place limits on the energies that an electron is allowed to have. The
mathematical representation of those energies results in regions of space called orbitals, which, as we will soon see,
can have different sizes and shapes. In order to distinguish between various orbitals and the electrons that occupy
them, scientists use quantum numbers. Quantum numbersspecify the properties of the atomic orbitals and the
electrons in those orbitals.Understanding quantum numbers is helped by an analogy. Let’s say you are attending
a basketball game. Your ticket may specify a gate number, a section number, a row, and a seat number. No other
ticket can have the same four parts to it. It may have the same gate, section, and seat number, but if so, it would
have to be in a different row. There are also four quantum numbers which describe the range of possible locations
for every electron in every atom. No two electrons in a given atom can have the same four quantum numbers. We