# Electrons in atoms

```ELECTRONS IN ATOMS
Chapter 5
Section Overview
• 5.1: Models of the Atom
• 5.2: Electron Arrangement in Atoms
• 5.3: Physics and the Quantum Mechanical Model
MODELS OF THE ATOM
Section 5.1
The Development of Atomic Models
• Atoms consist of protons, neutrons, and electrons.
• Rutherford’s atomic model could not explain the chemical
properties of elements.
• More models were needed that explained the behavior of
electrons within atoms.
The Development of Atomic Models
The Bohr Model
• Bohr proposed that an electron is found only in specific
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circular paths, or orbits, around the nucleus.
Each electron orbit in Bohr’s model has a fixed energy.
The fixed energies an electron can have are called energy
levels (ex. Rungs in a ladder: lowest rung equals
lowest energy level. People cannot move between
rungs, electrons cannot move between energy levels).
A quantum of energy is the amount of energy needed to
move an electron from one energy level to another.
Bohr’s model provided more insight, but still failed to
explain the energies absorbed and emitted by atoms with
more than one electron since he only used hydrogen in
his experiments.
The Quantum Mechanical Model
• Erwin Schrodinger used new theoretical calculations and
experimental results to create and solve a mathematical
equation describing the behavior of the electron in a
hydrogen atom.
• The quantum mechanical model comes from
mathematical solutions to the Schrodinger equation.
• It determined the allowed energies an electron can have
and how likely it is to find the electron in various locations
in the nucleus.
Atomic Orbitals
• An atomic orbital is often thought of as region of space in
which there is a high probability of finding an electron.
• For each principal energy level, there may be several
orbitals with different shapes and at different energy
levels.
• These energy levels within a principal energy level make
up energy sublevels.
• Each energy sublevel corresponds to an orbital a different
shape, which describes where the electron is likely to be
found.
Atomic Orbitals
• The numbers and kinds of atomic orbitals depend on the
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energy sublevel.
The lowest principal energy level (n =1) has only one sublevel,
called 1s.
The second principal energy level (n=2) has two sublevels, 2s
and 2p. 2p has higher energy than 2s. There are a total of four
orbitals in this level.
The third principal energy level (n=3) has three sublevels 3s,
3p, and 3d. There are a total of nine orbitals in this level.
The fourth principal energy level (n=4) has four sublevels 4s,
4p, 4d, and 4f. There are a total of sixteen orbitals in this level.
The maximum number of electrons that can occupy a principal
energy level is given by the formula 2n2.
Atomic Orbitals
Principal Energy
Level
Number of
Sublevels
Type of Sublevel
Maximum
Number of
Electrons
n=1
1
1s (1 orbital)
2
n=2
2
2s (1 orbital), 2p
(3 orbitals)
8
n=3
3
3s (1 orbital), 3p
(3 orbitals), 3d (5
orbitals)
18
n=4
4
4s (1 orbital), 4p
(3 orbitals), 4d (5
orbitals), 4f (7
orbitals)
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ELECTRON
ARRANGEMENT IN
ATOMS
Section 5.2
Electron Configurations
• In an atom, electrons and the nucleus interact to make the
most stab arrangement possible.
• The ways in which electrons are arranged in various
orbitals around the nuclei of atoms are called electron
configurations.
• The three rules (the aufbau principle, the Pauli exclusion
principle, and Hand’s rule) tell you how to find the electron
configuration of atoms.
Electron Configurations
• Aufbau Principle: Electrons occupy the orbitals of the
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lowest energy first.
The orbitals for any sublevel of a principal energy level
are always of equal energy.
Within a principal energy level, the s sublevel is always
the lowest-energy sublevel.
Pauli Exclusion Principle: An atomic orbital may have at
most two electrons.
To occupy the same orbital, two electrons must have
opposite spins; that is, the electron spins must be paired
(clockwise or counterclockwise).
Hund’s Rule: Electrons occupy orbitals of the same
energy in a way that makes the number of electrons with
the same spin direction as large as possible.
Electron Configurations
• The shorthand method for showing electron configuration
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involves writing the energy level and the symbol for the
sublevel.
The amount of electrons in that sublevel are represented
with a superscript.
Examples:
Hydrogen = 1s1
Helium = 1s2
Oxygen = 1s22s22p4
The sum of the superscripts equals the total number of
electrons in the atom.
Electron Configurations
• Example Problem: Phosphorus has an atomic number of
15. Write the electron configuration for the phosphorus
atom.
• Solution:
Atomic number = 15 = number of electrons
There is a max of two electrons per orbital (s=1x2, p=3x2,
d=5x2, f=7x2)
1s22s22p63s23p3
Exceptional Electron Configurations
• 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 configurations.
• These exceptions are due to subtle electron-electron
interactions in orbitals with very similar energies.
• Ex: Chromium
Incorrect = 1s22s22p63s23p63d44s2 (only keeping last s level
full)
Correct = 1s22s22p63s23p63d54s1 (keeping both d and s half
full)
PHYSICS AND THE
QUANTUM MECHANICS
MODEL
Section 5.3
Light
• The quantum mechanical model grew out of the study of
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light, which acts in waves.
The top of a wave is called the crest and the bottom is
called the trough.
The amplitude of a wave is a wave’s height from zero to
the crest.
The wavelength (λ) is the distance between the crests.
The frequency (ν) is the number of wave cycles to pass a
given point per unit of time. The SI unit is Hertz (Hz).
The product of wavelength and frequency always equals
a constant (ϲ), the speed of light.
ϲ = λν
Light
Light
• The wavelength and frequency of light are inversely
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proportional to each other.
For example, as the wavelength increases, the frequency
decreases.
Light consists of electromagnetic waves.
microwaves, infrared waves, visible light, ultraviolent
waves, X-rays, and gamma rays.
Sunlight consists of light with continuous range of
wavelengths and frequencies.
When sunlight passes through a prism, the difference
frequencies separate into a spectrum of colors (ex.
Rainbows).
Light
Atomic Spectra
• When atoms absorb energy, electrons move to higher
energy levels, and these electrons lose energy by emitting
an electric current through a gas in a neon tube
energizes the electrons of the atoms of the gas and
causes them to emit light).
• The frequencies of light emitted by an element separate
into discrete lines to give the atomic emission spectrum of
the element.
• No two atoms have the same emission spectrum.
• Atomic emission spectra are useful for identifying
elements (ex. Nitrogen gas gives off a yellowishorange light).
An Explanation of Atomic Spectra
• The lowest possible energy of the electron is its ground
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state where n=1.
Excitation of the electron by absorbing energy raises it to
an excited state with n = 2, 3, 4, 5, 6 and so on.
A quantum 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 electron.
Therefore, each transition produces a line of a specific
frequency in the spectrum.
An Explanation of Atomic Spectra: Hydrogen
Quantum Mechanics
• Albert Einstein proposed that light could be described as
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quanta of energy.
The quanta behave as if they were particles.
Light quanta are called photons.
Louis de Broglie proposed that particles of matter move in
a wavelike way and that all moving objects have wavelike
behavior.
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.
Quantum Mechanics
• Werner Heisenberg developed the Heisenberg
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uncertainty principle which states that it is impossible to
know exactly both the velocity and the position of a
particle at the same time.
This, however, is not true for ordinary sized objects like
cars.
It is only critical in dealing with small particles like
electrons.
Electrons have such a small mass that striking it with a
photon of light affects its motion in a way that can’t be
predicted precisely.
So, measuring the position of the electron changes its
velocity, which makes it uncertain.
Quantum Mechanics
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