Electrons are one of the elementary particles in the
universe. This means that to the knowledge of humanity, there is
no particle which makes up an electron. In other words, there is
nothing an electron can be divided into, it is "the smallest and
most basic constiuent of matter" (Wikipedia). Electrons,
along with protons and neutrons, compose atoms. To understand
quantum numbers and the basics of quantum mechanics, one must
understand the structure of an atom and how electrons interact
within it.
This home page will provide a brief overview of the structure of
the atom, various models of the atom, and an overview of the four
quantum numbers.
History of Atomic Theory
All matter is made up of atoms. This is something we now take as
a given, and one of the things you learn right back at the
beginning of high school or secondary school chemistry classes.
Despite this, our ideas about what an atom is are surprisingly
recent: as little as one hundred years ago, scientists were
still debating what exactly an atom looked like. See the
timeline on the right for a full breakdown on the history of the
atomic theory.
The most popular model for visualizing atoms is the Bohr Model,
which depicts electrons orbiting around the nucleus like planets
around a solar system. Bohr’s model didn’t solve all the atomic
model problems. It worked well for hydrogen atoms, but couldn’t
explain observations of heavier elements.
Heisenberg Uncertainty Principle- The exact position and velocity of an electron cannot
both be known at once. The equation below shows that unexpectedly, the more precisely we know the
position of an electron, the less precisely we know its velocity and vice versa.
The graphic demonstrates the Heisenberg Uncertainty Principle. On one atom we can clearly see the position of the electrons, but
this clarity makes it difficult to determine their velocities. On the other atom we can clearly see the direction and magnitude of the velocity of the electrons (indicated by the smear),
but this makes it harder to determine the exact position of the particles. Increased certainty for one values decreases the certainty for the other.
Photoelectric effect- Einstein demonstrated that when light of a certain frequency hits an atom
an electron is ejected. This showed that light can behave both as a wave and like a particle.
Oil Drop Experiment- Oil drops were sprayed above a positively charged plate containing a small hole. As the oil drops fell through the hole they acquired a negative charge. Gravity forced the drops downward. An applied electric field forced the drops upward. When a drop floated and was perfectly balanced, the weight of the drop was equal to the electrostatic force of attraction between the drop and the positive plate. Millikan found that the drops carried charges that were multiples of 1.60 x 10-19 C. He concluded that the charge of an electron must be 1.60 x 10-19 C. Using Thomson’s charge to mass ratio of the electron (1.76 x 108 C/gram), Millikan was able to determine the mass of an electron: Mass = 1.60 x 10-19 C /1.76 x 108 C/gram = 9.10 x 10-28 g = the mass of 1 electron
A total of four quantum numbers are used to describe completely
the movement and trajectories of each electron within an atom. The
combination of all quantum numbers of all electrons in an atom is
described by a wave function that complies with the Schrödinger
equation. Each electron in an atom has a unique set of quantum
numbers; according to the
Pauli Exclusion Principle,
no two electrons can share the same combination of four quantum
numbers.
Quantum numbers are important because they can be used to
determine the electron configuration of an atom and the probable
location of the atom's electrons. Quantum numbers are also used to
understand other characteristics of atoms, such as
ionization energy and the atomic radius.
