Chapter 4: Arrangement of Electrons in Atoms
I.
Development of a New Atomic Model
A. The Rutherford Model of the atom was a vast improvement over
previous models of the atom, but it was still incomplete. In the early
1900’s a new model of the atom, based on light absorption and
emission, was evolving.
B. Properties of Light.
1. Is light a wave or a particle? Before 1900 the answer was wave.
This changed when light was found to have characteristics of
particles as well.
2. The wave description of light.
a. Visible light is a form of electromagnetic radiation. EM
radiation is a form of energy that consists of oscillating electric
and magnetic fields that are at 90o to one another and direction
of movement.
b. Other forms of EM radiation are gamma rays, X-rays, UV, IR,
Radar, Microwaves, Radio, and TV. Together these forms make
up the electromagnetic spectrum. Refer to Figure 1 on page 98.
c. All waves can be described using 4 terms:
i. Amplitude (A): Height of a wave.
ii. Wavelength (): Distance between 2 successive crests.
(usually measured in nm, cm, or m)
iii. Frequency (): number of waves that pass through a
given point in a given period of time. (measured in
waves/second or Hertz, Hz)
iv. Speed (c): is equal to wavelength * frequency. (The
speed of light in a vacuum is 3.00 * 108 m/s)
d. Because of the relationship c=, and the fact that c is
constant, we can infer that wavelength is inversely proportional
to frequency. (High frequency, short wavelength and vice
versa.)
C. The Photoelectric Effect
1. In the early 1900’s, conducted experiments that could not be
explained using the wave theory of light.
a. One experiment involved the photoelectric effect. The
photoelectric effect is the emission of electrons from a
metal when light shines on the metal. Figure 3 on page 99.
b. For a specific metal no electrons were emitted if the light
was below a certain frequency, regardless of how long the
2.
light was shone. The wave theory predicted that light of
any frequency will eject an electron.
The Particle Description of Light
a. Quantum Theory
i. The photoelectric effect can be explained by the theories of
Max Planck. He proposed that energy can only be absorbed
or emitted in small, specific sized amounts, which he called
quanta. (Ramp vs. Stairs)
ii. A quantum is the minimum quantity of energy that can be
lost or gained.
iii. Planck proposed that the relationship between energy and
frequency is E=h. E is energy (in joules), h is Planck’s
constant (6.63 * 10-34 J*s), and  is the frequency (in Hz).
iv. In 1905 Albert Einstein proposed that light has a dual waveparticle nature (it behaves like both). He stated that each
particle of light carries a quantum of energy. He called them
photons. A photon is a particle of EM radiation that has
zero mass and carries a quantum of energy. He used the
Quantum Theory to explain the photoelectric effect. In
order for an electron to be ejected it must be hit by a photon
that has the minimum amount of energy required to knock
the electron loose. If the photon is below the minimum
frequency, the electron will not be ejected.
D. Hydrogen Atom Line Emission Spectrum
1. Another problem that could not be explained by the wave theory of
light was the line spectrum of the hydrogen atom.
2. A line spectrum is produced when a current is passed through a
sample of hydrogen. The energy emitted by the sample is then
passed through a prism. The resulting separation of light is
characteristic of the substance. White light will give a continuous
spectrum.
3. Niels Bohr solved the puzzle of the line spectrum in 1913. He
proposed a new model of the atom.
4. His model of the atom was called the planetary model. The nucleus
is at the center of the atom (like the sun). The electrons float
around the nucleus in orbits (like the planets).
5. The line spectrum said to be caused by the electrons (in the ground
state) absorbing energy, “jumping” to a higher energy state (excited
state). When the electron “falls” back to the ground state, it
releases the energy as a photon. Because the photon has a specific
energy, it has a specific frequency. Because it has a specific
frequency, it has a specific wavelength, and therefore, a specific
color. See Figure 8 on page 102.
6. Bohr used this information to correctly predict the line spectrum of
hydrogen. However, he could not correctly predict line spectra for
other elements. Why? Interference from other electrons.
II. Quantum Model of the Atom
A. Electrons as Waves
1. In 1924 Louis de Broglie proposed that electrons have the same
dual wave-particle nature that light does.
2. Many experiments involving diffraction and interference confirmed
that electron beams act like waves.
A. Heisenberg’s Uncertainty Principle
1. H.U.P. it is impossible to determine simultaneously both the
position and the velocity of an electron or any other particle.
2. Was proposed in 1927 by Werner Heisenberg. His idea is based on
the fact that electrons are detected by interactions with photons.
Because these photons knock the electrons off course, we have an
uncertainty in locating them.
3. H.U.P. is only relevant with very small particles.
B. Schrodinger Wave Equation
1. Developed in 1926 by Erwin Schrodinger.
2. Quantized the energy of electrons. Only certain energies and
therefore, frequencies are allowed. It solved the problem brought
about by H.U.P. Together, these two provide the basis for the
Quantum Theory.
3. The Q.T. describes the wave properties of electrons.
4. By solving the Schrodinger Equation, the probability of finding an
electron at a given place around the nucleus is found. These
probabilities are used to form atomic orbitals.
5. An Atomic Orbital is a three dimensional region around the
nucleus that indicates the probable location of an electron.
C. Atomic Orbitals and Quantum Numbers
1. In order to completely describe orbitals we use Quantum Numbers,
which are solutions to the Schrodinger Equation.
2. Quantum Numbers specify the properties of atomic orbitals and
the properties of electrons in orbitals. There are 4 QN’s.
a. Principle Quantum Number (n): indicates main energy level.
b. Angular Momentum Quantum Number (l): indicates the shape
of the orbital.
c. Magnetic Quantum Number (m): indicates the orientation of an
orbital around the nucleus.
d.
3.
4.
Spin Quantum Number (ms): indicates which of the two
fundamental spins an electron has.
Values for the QN’s:
a. n: only positive integers (ex. 1,2,3,4, etc)
b. l: 0, and all integers up to n-1; (in the n=4 energy level, the
values for l are 0,1,2,3). The total number of orbital shapes is
equal to the value of n. 0 corresponds to s (spherical), 1 to p
(dumbbell), 2 to d, and 3 to f.
c. m: 0, and +/- l. (if the value of l=1, values for m are -1,0,+1).
d. ms: +/- 1/2, one or the other, that’s it. An orbital can have a
max of 2 electrons, and they must have opposite spins.
Meaning of QN’s
a. The total number of sublevels in an energy level is equal to n.
First energy level, 1 type of orbital. 2 has 2, 3 has 3, etc.
b. The number of orbitals in a sublevel are as follows: an s
sublevel has 1 s orbital; a p sublevel has 3 p orbitals; d has 5; f
has 7.
c. The max number of electrons in any orbital is 2. The max
number of electrons in a sublevel is 2* the number of orbitals in
that sublevel. For example, # of orbitals in a p sublevel is 3, so
max # of electrons is 6.
d. The quantum numbers for a specific electron gives the
“Address” of the electron, telling us where it “lives”.
III. Electron Configurations and Orbital Diagrams
A. Electron configurations & Orbital Diagrams give us the
arrangement of the electrons in an atom. Generally, we will be
concerned with the ground state situation. They are set up by following
3 rules.
B. The Aufbau Principle
1. The Aufbau Principle states that an electron occupies the lowest
energy orbital available to it. In other words, start by filling the
lowest energy orbitals available and work your way up.
2. There is a specific order of energies of orbitals. (1s, 2s, 2p, 3s, 3p,
4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, etc.) Figure 16 on page 111.
3. There are exceptions to the Aufbau Principle. They are Cr and
down, and Cu and down. Cr: [Ar] 4s13d5; Cu: [Ar] 4s13d10.
C. The Pauli Exclusion Principle
1. The Pauli Exclusion Principle states that no two electrons may
have the exact same set of quantum numbers. In other words,
2.
ANY orbital can have a maximum of 2 electrons and if there are
two they must be spinning in opposite directions.
We will indicate spins using arrows.
D. Hund’s Rule
1. Hund’s Rule states that orbitals of equal energy are each occupied
by one electron before any orbital is occupied by a second electron,
and all electrons in singly occupied orbitals must have the same
spin.
2. “One electron in each before pairing occurs.”
E.
Orbital Diagrams
1. In orbital diagrams we represent each orbital with a box. Equal
energy orbitals are represented by connected boxes. The electrons
are represented by arrows, which point up or down, depending on
spin. The boxes are labeled to indicate which orbitals the boxes
represent.
2. The easiest way to learn them is to practice, so do them for the
following elements: H, He, Li, Be, B, C, N, O, F, Ne.
F.
Electron Configurations
1. In electron configurations we are not concerned about the actual
orbitals, but merely the sublevels.
2. It is a short-hand form of orbital diagrams.
3. Practice: same as above, without looking at answers from above.
G. Abbreviated Electron Configurations
1. In many situations, the configurations are very, very long. We also
are only really concerned with the outermost, or valence electrons.
We solve this problem by developing a system that only show the
valence electrons.
2. To do this we use the Noble Gas Core. Noble Gases are in
Group 8A. The Noble Gas Core represents the inner electrons that
are not valence.
3. To determine the core, we count backward by atomic number until
we get to a Noble Gas. The symbol for that Noble Gas is placed in
brackets and represents the inner electrons.
4. We then represent the rest of the electrons in the same manner as
regular configurations.
5. Practice doing configs for Ra, Rb, Ga, Ti, V, Y, and Kr.