Electrons in Atoms
Electrons in Atoms
The scale model shown is a
physical model. However,
not all models are physical.
In fact, several theoretical
models of the atom have
been developed over the
last few hundred years. You
will learn about the
currently accepted model of
how electrons behave in
The Development of Atomic Models
◦ What was inadequate about Rutherford’s atomic
Rutherford’s atomic model could not explain the
chemical properties of elements.
Rutherford’s atomic model could not explain why objects
change color when heated.
The timeline shows the development of atomic models
from 1803 to 1911.
The timeline shows the development of atomic models
from 1913 to 1932.
The Bohr Model
◦ What was the new proposal in the Bohr model of the
◦ Bohr proposed that an electron is found only in
specific circular paths, or orbits, around the
Each possible electron orbit in Bohr’s model has a
The fixed energies an electron can have are called energy
levels or shells. See periodic table
A quantum of energy is the amount of energy required to
move an electron from one energy level (shell) to another
Like the rungs of the
strange ladder, the energy
levels in an atom are not
The higher the energy level
occupied by an electron,
the less energy it takes to
move from that energy
level to the next higher
The Quantum Mechanical Model
◦ What does the quantum mechanical (electron cloud)
model determine about the electrons in an atom?
◦ The quantum mechanical model determines the
allowed energies an electron can have and how
likely it is to find the electron in various locations
around the nucleus.
The exact location of an electron cannot be known
with certainty because to do so you would have to
interfere with it (Heisenberg Uncertainty Principle).
Austrian physicist Erwin Schrödinger (1887–1961) used
new theoretical calculations and results to devise and
solve a mathematical equation describing the behavior
of the electron in a hydrogen atom.
The modern description of the electrons in atoms, the
quantum mechanical model, comes from the
mathematical solutions to the Schrödinger equation.
The propeller blade has the same probability of
being anywhere in the blurry region, but you cannot
tell its location at any instant. The electron cloud of
an atom can be compared to a spinning airplane
In the quantum mechanical (electron cloud) model, the
probability of finding an electron within a certain
volume of space surrounding the nucleus can be
represented as a fuzzy cloud. The cloud is more dense
where the probability of finding the electron is high.
◦ How do sublevels of principal energy levels differ?
An atomic orbital is often thought of as a region of
space in which there is a high probability of finding an
Each energy sublevel corresponds to an orbital of a
different shape, which describes where the electron is
likely to be found.
Different atomic orbitals are denoted by letters. The s
orbitals are spherical, and p orbitals are dumbbellshaped.
Four of the five d orbitals have the same shape but
different orientations in space.
F orbitals are weird.
The numbers and kinds of atomic orbitals depend on
the energy sublevel.
The maximum number of electrons per
orbital is two. So….
◦ n = principal energy level
◦ n = the number of sublevels per principal energy
◦ n2 = the number of orbitals per principal energy
◦ 2n2 = the number of electrons per principal energy
Make a chart
So what is an electron doing in an orbital?
◦ Spinning while moving. Either clockwise or
◦ Electrons occupying the same orbital spin in
Electrons can be described by four quantum
◦ n= principal quantum number (energy level)
◦ l= orbital quantum number (sublevel)
◦ ml= magnetic quantum number (orbital orientation
◦ ms= spin quantum number (+ or -)
No two electrons can have the same four
quantum numbers (Pauli Exclusion Principle).
If this rock were to tumble
over, it would end up at a
lower height. It would have
less energy than before,
but its position would be
more stable. You will learn
that energy and stability
play an important role in
determining how electrons
are configured in an atom.
◦ What are the three rules for writing the electron
configurations of elements?
The ways in which electrons are arranged in various
orbitals around the nuclei of atoms are called electron
Three rules—the aufbau principle, the Pauli exclusion
principle, and Hund’s rule—tell you how to find the
electron configurations of atoms.
◦ Aufbau Principle
According to the aufbau principle, electrons occupy
the orbitals of lowest energy first. In the aufbau
diagram below, each box represents an atomic orbital.
◦ Pauli Exclusion Principle
According to the Pauli exclusion principle, an atomic
orbital may describe at most two electrons. To occupy
the same orbital, two electrons must have opposite
spins; that is, the electron spins must be paired.
◦ Hund’s Rule
Hund’s rule states that electrons occupy orbitals of the
same energy in a way that makes the number of
electrons with the same spin direction as large as
The principle energy level is the first number,
the sublevel is the letter (s,p,d or f) and the
number of electrons in the sublevel is the
Number of electrons in sublev
Principal energy level
Type of sublevel
Orbital Filling Diagram
Exceptional Electron Configurations
◦ Why do actual electron configurations for some
elements differ from those assigned using the
◦ Some actual electron configurations differ from
those assigned using the aufbau principle because
half-filled sublevels are not as stable as filled
sublevels, but they are more stable than other
Exceptions to the aufbau
principle are due to subtle
in orbitals with very similar
Copper has an electron
configuration that is an
exception to the aufbau
Neon advertising signs are
formed from glass tubes
bent in various shapes. An
electric current passing
through the gas in each
glass tube makes the gas
glow with its own
characteristic color. You will
learn why each gas glows
with a specific color of light.
◦ How are the wavelength and frequency of light
The amplitude of a wave is the wave’s height from zero to
The wavelength, represented by (the Greek letter
lambda), is the distance between the crests.
The frequency, represented by (the Greek letter nu), is
the number of wave cycles to pass a given point per unit
The SI unit of cycles per second is called a hertz (Hz).
The product of the frequency and wavelength always
equals a constant (c), the speed of light.
The wavelength and frequency of light are inversely
proportional to each other.
According to the wave model, light consists of
Electromagnetic radiation includes radio waves,
microwaves, infrared waves, visible light, ultraviolet
waves, X-rays, and gamma rays.
All electromagnetic waves travel in a vacuum at a speed of
2.998 108 m/s.
Sunlight consists of light with a continuous range of
wavelengths and frequencies.
When sunlight passes through a prism, the different
frequencies separate into a spectrum of colors.
In the visible spectrum, red light has the longest
wavelength and the lowest frequency.
The electromagnetic spectrum consists of radiation
over a broad band of wavelengths.
◦ What causes atomic emission spectra?
◦ When atoms absorb energy, electrons move into
higher energy levels. These electrons then lose
energy by emitting light when they return to lower
A prism separates light into the colors it contains. When
white light passes through a prism, it produces a rainbow
When light from a helium lamp passes through a
prism, discrete lines are produced.
The frequencies of light emitted by an element
separate into discrete lines to give the atomic
emission spectrum of the element.
An Explanation of Atomic Spectra
◦ How are the frequencies of light an atom emits
related to changes of electron energies?
In the Bohr model, the lone electron in the
hydrogen atom can have only certain
When the electron has its lowest possible
energy, the atom is in its ground state.
Excitation of the electron by absorbing
energy raises the atom from the ground
state to an excited state.
A quantum of energy in the form of light
is emitted when the electron drops back to
a lower energy level.
◦ The light emitted by an electron moving from a
higher to a lower energy level has a frequency
directly proportional to the energy change of the
Therefore each transition produces a line of a specific
frequency in the spectrum.
The three groups of lines in the hydrogen spectrum
correspond to the transition of electrons from higher
energy levels to lower energy levels.
◦ How does quantum mechanics differ from classical
In 1905, Albert Einstein successfully explained
experimental data by proposing that light could be
described as quanta of energy.
The quanta behave as if they were particles.
Light quanta are called photons.
In 1924, De Broglie developed an equation that
predicts that all moving objects have wavelike
Today, the wavelike properties of beams of electrons
are useful in magnifying objects. The electrons in an
electron microscope have much smaller wavelengths
than visible light. This allows a much clearer enlarged
image of a very small object, such as this mite.
◦ Classical mechanics adequately describes the
motions of bodies much larger than atoms, while
quantum mechanics describes the motions of
subatomic particles and atoms as waves.
The Heisenberg uncertainty principle states that it is
impossible to know exactly both the velocity and the
position of a particle at the same time.
This limitation is critical in dealing with small particles
such as electrons.
This limitation does not matter for ordinary-sized object
such as cars or airplanes.
The Heisenberg Uncertainty Principle