Chapter 13 – Electrons in Atoms
Part 1 – Notes: Revisiting the History of Atomic Theory and Orbitals
Objectives: Summarize the development of the atomic theory
from Bohr forward.
Explain the significance of quantized energies of electrons in relation to
the quantum mechanical model.
Identify, define, and explain: energy level, quantum, quantum mechanical
model (wave mechanical model), atomic orbitals, quantized, sublevel, ground
state, excited state, probability, and principal quantum number.
Explain Aufbau Principle, Hund’s Rule, and Pauli Exclusion Principle and
how they are used to determine the location of an electron in an atom.
List, describe, and differentiate between s, p, d, and f atomic orbitals.
Relate the principal quantum number to the number of orbital types in an
atom and to the number of individual orbitals in a given energy level.
Text Reference: Section 13.1 – pages 361-366
We left off with Rutherford’s model of the atom: a small dense nucleus made
of protons with electrons outside the nucleus.
The existence of the neutron was added to the atom in 1932.
Neils Bohr – 1885 – 1962 – Danish physicist – student of Rutherford
∑ The Planetary Motion Model – proposed in 1913
o Electrons are arranged in concentric circular paths, or orbits, around
the nucleus.
∑ The question that needed to be answered was “why don’t the electrons crash
into the nucleus?”
∑ Bohr’s answer:
The energies of electrons are QUANTIZED – meaning only certain values are
allowed.
Energy level –
∑ The rungs of a ladder are somewhat analogous to the fixed energy levels
of the electrons. The lowest rung corresponds to the lowest energy
level. A person can stand on step one or step two – but not on step
one-and-a-half.
Quantum – a quantum of energy is the amount of energy required to move an
electron from its present level to the next higher one
But the Bohr model of the atom was incorrect. Two young physicists,
Louis Victor de Broglie and Erwin Schrödinger, suggested that just as
light exhibits characteristics of waves and particles, the electron may also
exhibit both those characteristics. The idea that an electron, a particle,
could exhibit properties of a wave was revolutionary.
Erwin Schrödinger (1887 – 1961) and Louis Victor de Broglie
Model: The Wave Mechanical Model (Also the Quantum Mechanical Model)
∑ Schrödinger used the new quantum theory to write and solve mathematical
equations to describe the location and energy of an electron in an atom.
∑ The model is derived from mathematical solutions to the Schrödinger
equation.
∑ Schrödinger’s model is primarily mathematical; there are few (if any)
analogies in real life.
The Quantum Mechanical Model – a modern description of electrons in atoms
∑ It incorporates both wave-particle theory and probability into its description
of electron behavior.
∑ Energies of electrons are restricted to certain values – similar to Bohr’s
model.
∑ The path of an electron around a nucleus is not exact. Instead there
is a region of probability where an electron is most likely to be found.
The idea is based around the likelihood of finding an electron in a certain
region or position.
∑ This probability can be portrayed as a blurry cloud of negative charge.
The CLOUD is most dense where the probability of finding the electron is
large. The cloud is least dense where the probability of finding the
electron is small. Hence, it is difficult to say where the electron
cloud ends. There is no edge. There is even a probability of finding
the electron a great distance away from the nucleus.
∑ The path of an electron is not precisely predictable; however the work
of deBroglie and Schrödinger led to orbitals.
Atomic Orbital: An orbital is a probability map, a region in which
the electron has a 90% ( or 95%) probability of being found.
Principal energy levels –
Principal Quantum Number: refers to the energy level in which an electron
is located – designated “n”
∑ Principal quantum numbers are positive integers, beginning with 1
∑ 1 is the lowest energy level, and electrons in this level have a principal
quantum number of n = 1
∑ The higher the n. the higher the average energy of the electrons in the
energy level.
∑ The higher the n, the greater the average distance of the electron from
the nucleus.
Sublevels –
∑ The number of orbitals inside the energy level depends upon the energy
level itself.
∑ For n = 1, there is 1 type of sublevel. For n = 2, there are two
types of sublevels/atomic orbitals.
∑ The number of atomic orbitals in a given energy level is equal to the principal
quantum number.
There are four basic types of orbitals: s, p, d, and f. There are additional
orbitals designated g, h, i, j, k, …
Shape Groups of… Begin
where? Relative energy
s-orbital
p-orbital
d-orbital
f-orbital
Within a given energy level, the energy increases accordingly: s < p <
d < f
∑ but this order does not hold true when you are talking about different
energy levels.
The size of the orbital increases with each energy level – but the shape
remains the same.
∑ A 1s orbital and a 2s orbital are both spherical, but the 1s orbital is
smaller than the 2s orbital.
Relationship between n and number of different types of orbitals: n
= number of sublevels = # of orbital types
Relationship between n and the number of orbitals: # of orbitals =
n2
If each orbital can hold 2 electrons, relationship between n and number of
orbitals: # of possible electrons = 2 n2
Rules to Remember
1. Energy levels, n, increase by integer values.
2. The number of orbitals per energy level is equal to
n2. the first energy level will have one orbital. The second
energy level, n = 2, will have 4 orbitals. The third energy level,
n = 3, will have nine orbitals. And so on.
3. Every energy level has an s orbital. The s-orbital
is sphere shaped.
4. Energy levels n = 2 and higher contain a set of three
p-orbitals: px, py, and pz. The p-orbitals have two lobes.
5. Energy levels n = 3 and higher contain a set of five
d-orbitals: dxy, dxz, dyz, dz2, and dx2-y2 that have four lobes.
6. Energy levels n = 4 and higher contain a set of seven
f-orbitals. The subscripts are not important for our purposes; just
know the total number. They also have shapes more complex than can
be simply described.
7. Aufbau Principle (Building Up) –
8. Pauli Exclusion Principle –
9. Hund’s Rule –
Electron Configuration Notation: a bc
a =
b =
c =
Chapter 13 – Electrons in Atoms
Part 1 – Assignment: Revisiting the History of Atomic Theory and Orbitals
Provide complete answers to the following questions.
1. Why was Bohr’s theory for the hydrogen atom initially
accepted, and why was it ultimately discarded?
2. What major assumptions (that was analogous to what had
already been demonstrated for electromagnetic radiation) did de Broglie and
Schrödinger make about the motion of electrons?
3. Discuss briefly the difference between an orbit (as
described by Bohr for hydrogen) and an orbit (as described by the more modern
picture of the atom).
4. In general terms, explain how the quantum mechanical
model of the atom describes the electron structure of an atom.
5. How many orbitals are in the following sublevels:
3p = ____________________
2s = ____________________ 4f =
____________________
4p = ____________________
3d = ____________________ 6g =
____________________
6. How did Bohr answer the objection that an electron traveling
in a circular orbit would radiate energy and fall into the nucleus?
7. What is the significance of the border of the electron
cloud?
8. What is an atomic orbital?
Chapter 13 – Electrons in Atoms
Part 2 – Notes: Electron Configurations and Orbital Diagrams
Objectives: Apply the Aufbau principle, the Pauli Exclusion
Principle, and Hund’s Rule in writing electron configurations of elements.
Identify, define, and, explain: electron configuration,
Aufbau principle, Hund’s Rule, Pauli Exclusion Principle, and orbital diagram.
Explain why all of the 3rd energy level does not fill
before the 4th energy level starts to fill.
Text Reference: Section 13.2 (Part) – pages 367-369
Key Items to Keep in Mind:
1. Energy levels, n, increase by integer values.
2. The number of orbitals per energy level is equal to n2. the first
energy level will have one orbital. The second energy level, n = 2,
will have 4 orbitals. The third energy level, n = 3, will have nine
orbitals. And so on.
3. Every energy level has an s orbital. The s-orbital is sphere shaped.
4. Energy levels n = 2 and higher contain a set of three p-orbitals: px,
py, and pz. The p-orbitals have two lobes.
5. Energy levels n = 3 and higher contain a set of five d-orbitals: dxy,
dxz, dyz, dz2, and dx2-y2 that have four lobes.
6. Energy levels n = 4 and higher contain a set of seven f-orbitals.
The subscripts are not important for our purposes; just know the total number.
They also have shapes more complex than can be simply described.
7. Aufbau Principle – Electrons fill orbitals from lowest to highest energy.
8. Pauli Exclusion Principle – No two electrons in the same atom can have
the same four quantum numbers. In other words, an orbital can hold
at most two electrons and if there are two electrons, they have paired spins.
9. Hund’s Rule – When electrons occupy a set of degenerate orbitals, one
electron enters each orbital until all orbitals contain one electron with
their parallel spins.
Electron Configurations utilize the (first) principal quantum number, n,
and the second quantum number, l, along with an integer superscript to represent
the organization of an atom’s electron from lowest to highest energy.
Example Electron Configuration: 1 s2 (read
“one s two” NOT “one s-squared”)
The 1 represents
The s represents
The superscript 2 indicates
Another way to represent the electrons of an atom is through the use of an
orbital diagram, also known as a box diagram. Orbital diagrams are
drawn with the first two numbers above the box (or series of boxes).
One or two arrows are placed in the box to indicate the number of electrons
present. If there are two arrows in the box, representing two electrons
in the orbital, they must have opposite spins (Pauli Exclusion Principle).
The arrows are pointed in opposite directions to represent the opposite spins.
Electron Configuration and Orbital Diagrams for the First 18 Elements
At this time, all elements are considered to be in their ground state, the
state of least energy.
Hydrogen: The neutral hydrogen contains 1 electron.
Helium: Recall the Pauli Exclusion Principle
as you draw in the second electron.
Lithium: The first energy level fills and then the second
energy level starts to fill; recall Aufbau Principle.
Beryllium: The fourth electron completes the 2s orbital.
Boron: Boron has 5 electrons, four of
which fill the 1s and the 2s orbitals. The fifth electron must fill
the orbital of the next highest energy, the 2p. Since there is a group
of three p-orbitals, it is uncertain which fills first, by convention, it
is assumed that the 2 px orbital fills first.
Carbon: Carbon has six electrons. Two occupy the
2p orbital. Recall Hund’s Rule. For reasons not considered here,
in the separate 2p orbitals, the electrons have the same spin.
When the electron configuration is written with a single term to indicate
the two p-orbitals, it is understood that the electrons are in separate orbitals,
even though the configuration does not indicate it; it may be written this
way because we know that Hund’s Rule must be fulfilled.
Nitrogen: Nitrogen has 7 electrons. Each of the electrons
in the 2p orbitals will have the same spin.
Oxygen: Oxygen has 8 electrons. The eighth electron
is paired with the 5th in the 2px electron; each has opposite spin.
Fluorine: Fluorine has 9 electrons. The 9th electron
is paired with the 6th electron in the 2py orbital; each has opposite spin.
Neon: Neon has 10 electrons and they
completely fill the orbitals of the first and second energy levels.
Sodium: Sodium has 11 electrons. The 11th electron
must enter the 3rd energy level, since the 2nd level is filled.
Magnesium: Magnesium has 12 electrons.
Aluminum: Aluminum has 13 electrons. The 13th electron
starts to fill the 3p orbitals.
Silicon: Silicon has 14 electrons.
When filling the 3p orbitals, remember Hund’s Rule.
Phosphorus: Phosphorus has 15 electrons.
Sulfur: Sulfur
has 16 electrons.
Chlorine: Chlorine has 17 electrons.
Argon:
Argon has 18 electrons.
What happens after the 18th electron fills into the 3p sublevel? What
orbital do you think will fill next?
According to the Aufbau principle, we know orbitals fill in order from low
to high energy. Examine the energy diagram to determine which orbital
fills next.
Chapter 13 – Electrons in Atoms
Part 2 – Assignment: Electron Configurations and Orbital Diagrams
Answer the following questions. Be complete and neat.
1. Arrange the following sublevels in order of decreasing
energy: 2p, 3s, 3p, 3d, and 4s
__________ __________
__________ __________ __________
Explain why the above trend is true.
2. Why does one electron in a potassium atom go into the
fourth energy level instead of squeezing into the third energy level along
with the eight electrons already present?
3. What is meant by 3p3? Draw an orbital diagram
to help explain your answer.
4. What is the maximum number of electrons that can go
into each of the following sublevels?
a. 2s __________
b. 3p __________
c. 4s __________
d. 3d __________
e. 4p __________
f. 5s __________
g. 4f __________
h. 5p __________
i. 7g __________
5. Which of these orbital designations are invalid:
4s 3f 2d 3d
4g 6g 1p
6. How many paired electrons are there in an atom of each
of the following:
a. helium
b.
boron
c. sodium
d.
oxygen
7. An atom of an element has two electrons in the first
energy level and five electrons in the second energy level. Write the
electron configuration for the atom. State the name of the element.
How many unpaired electrons does an atom of this element have?
8. An atom of a specific element has two electrons in the
first energy level, 8 electrons in the second energy level, and five electrons
in the third energy level. Write the electron configuration for the
atom. State the name of the element. How many unpaired electrons
does an atom of this element have?
Chapter 13 – Electrons in Atoms
Part 3 – Notes: More Electron Configurations & Valence Electrons
Objectives: Apply the Aufbau principle, Hund’s Rule, and
Pauli Exclusion Principle in writing electron configurations of elements.
Identify, define, and, explain: electron configuration,
Aufbau principle, Hund’s Rule, Pauli Exclusion Principle, and valence electron.
Explain why all of the 3rd energy level does not fill
before the 4th energy level starts to fill.
Text Reference: Section 13.2 (Part) – pages 367-370
You know the electron configuration for argon is ____________________________________________________.
You also know that the third energy level, n = 3, has three different sublevels:
s, p, and d.
Because s and p orbitals of the third energy level are filled in argon, you
might expect that the 19th electron of element 19, potassium, to be placed
into a 3d orbital; however, experiments show that the chemical properties
of potassium are very similar to lithium and sodium. Chemists associate
similar chemical properties with similar valence-electron arrangements; hence
it is predicted that the outer electrons of potassium be s1, resembling sodium
(3s1) and lithium (2s1). We expect the last electron in potassium to
occupy the 4s orbital instead of one of the 3d orbitals. This means
that the fourth principal energy level begins to fill before the third energy
level has been completed.
Examine the diagram of energy levels and orbitals. How is it that the
4th energy level begins to fill before the third energy level has been completed?
Potassium:
Calcium:
Now, scandium has 21 electrons. Where does the 21st electron go?
Careful studies of energies of ground state atoms have given a filling order
that is represented in the energy diagram.
Scandium:
Note the remaining electron configurations for the transition metals in the
fourth period will follow a similar pattern.
After 3p fills, _______________ fills, followed by _______________, and _______________.
Let’s put the filling order to use as we write the ground state electron
configurations for the following atoms.
Titanium:
Nickel:
Copper:
Zinc:
Arsenic:
Krypton:
Molybdenum:
Lead:
Tungsten:
Valence Electrons
Valence electrons - electrons in the outermost orbitals of an atom
Examples 1 and 2
Electron configuration of: Nitrogen Phosphorus
Highest energy level
Electrons in the highest energy level
Total number of valence electrons
Examples 3 and 4
Electron configuration of: Sodium Lithium
Highest energy level
Electrons in the highest energy level
Total number of valence electrons
The valence electrons are the most significant to chemists because those
are the electrons involved when atoms attach to each other (form bonds).
The inner electrons are known as core electrons. The core electrons
are not involved in bonding atoms to one another.
If you study the configurations of the elements in the same groups you will
find that, with the exception of helium, elements of the same group…
EXAMPLES 5 – 10:
Element Symbol Group Configuration
of Valence Electron
Neon
Argon
Magnesium
Calcium
Sulfur
Selenium
ELEMENTS WITH THE SAME NUMBER OF VALENCE ELECTRONS (elements in the same
family) EXHIBIT SIMILAR CHEMICAL BEHAVIOR!!!!!
Chapter 13 – Electrons in Atoms
Part 3 – Assignment: More Electron Configurations & Valence Electrons
Write the electron configurations for the following elements. Also,
write the number of valence electrons in each.
1. zirconium
2. hafnium
3. rutherfordium
4. silver
5. tin
6. ytterbium
7. uranium
8. antimony
9. How many electrons are in the second energy level of
an atom of each of the following elements?
a. chlorine
b. phosphorous
c. potassium
10. Write the electron configuration for an arsenic atom.
Calculate the total number of electrons in each energy
level.
State which energy level(s) is/are not full.
11. Ms. Anderson’s favorite equation is that of an active
metal + water. You react sodium with water and you get sodium hydroxide
and hydrogen gas. You react potassium with water and you get potassium
hydroxide and hydrogen gas. What do you get if you react lithium with
water? Why is there similarity between the products and also the equations
(including the coefficients) when you react an alkali metal with water?
Chapter 13 – Electrons in Atoms
Part 4 – Notes: Anomalous and Abbreviated Electron Configurations
Objectives: See objectives from Chapter 13 Part 2 and 3.
Write abbreviated configurations for
elements.
Explain why the electron configurations
for the chromium and copper columns do not fit the standard pattern.
Correctly write the electron configurations for chromium molybdenum, tungsten,
copper, silver, and gold, and explain why it is written in such a manner.
Text Reference: Section 13.2 (Part) – pages 367-370
Anomalies of Electron Configurations
Based on your current knowledge, write the electron configuration of chromium
and copper.
Chromium:
Copper:
These electron configurations are actually INCORRECT!!! Take a moment
to cross them out.
Atoms in the ground state have the lowest possible energy. Atoms want
to have the lowest possible energy. That is why some of them form ions
and some form covalent compounds, to obtain a state of minimum energy.
When electrons fill into the orbitals, they do so in such a manner as to
minimize the energy of the atom. There is a special stability that
comes from a half-full or a filled energy level. It is this special
stability that will give use the correct electron configuration for chromium
and copper.
Chromium’s correct electron configuration is:
Note, this happens because
Copper’s correct electron configuration is:
Note, this happens because
Note, the 3d orbital is completely filled and the 4s orbital is half-filled.
It is more stable to have the 3rd energy level completed than it is to have
the 3rd energy level missing one and the 4th energy level just started.
So, for copper, the 3rd energy level is completed which leads to greater
stability (low energy) to the atom.
There are a number of other anomalies that occur throughout the periodic
table. You will be responsible for the anomalies of chromium, copper,
molybdenum, silver, tungsten, and gold. Mo, W, Ag, and Au follow the
same valance configuration as chromium and copper, based upon the column
in the periodic table.
There are other anomalies for which you are not held responsible.
Note the following rules for writing the electron configurations:
1. In a principal energy level that has d orbitals, the
s-orbitals from the next level before the d-orbital in the current level.
2. After lanthanum, which has the electron configuration
[Xe] 6s2 5d1, a group of fourteen elements called the lanthanide series occurs.
This series of elements corresponds to the filling of the seven 4f orbitals.
3. After actinium, which has the electron configuration
[Rn] 7s2 6d1, a group of fourteen elements known as the actinide series occurs.
This series corresponds to the filling of the seven 5f orbitals.
Abbreviated electron configurations
Sometimes writing electron configurations is a long and tedious process.
Is there a shorter way???
The knowledge of valence electrons, electron configurations, and noble gases
may be used to write abbreviated electron configurations. Abbreviated
electron configurations allow us to write electron configurations quickly.
Electron configuration for NEON:
Electron configuration for MAGNESIUM:
Abbreviated configuration for MAGNESIUM:
Write the abbreviated electron configuration for the following elements:
Sodium:
Aluminum:
Silicon:
Phosphorus:
Sulfur:
Argon:
Note that for all of the elements except the noble gases, the electrons represented
after the noble gas are also the valence electrons. The noble gas core
used is actually abbreviating the core electrons.
Ground State versus Excited State
Hydrogen has only one single electron and this electron fills into the lowest
energy level. Although only the first energy level is used, hydrogen
still has a full set of atomic orbitals that are not used in the GROUND STATE
of hydrogen. However, in the EXCITED STATE, the single electron will
go into a higher energy level. So, even though in the ground state,
only the first energy level is used, hydrogen has the other atomic orbitals
so they may be used when necessary – in the excited state or during bonding.
Chapter 13 – Electrons in Atoms
Part 4 – Assignment: Anomalous, and Abbreviated Electron Configurations
For each of the following elements, write the complete electron configuration
and list the number of valence electrons.
1. thorium
2. tellurium
3. technetium
4. mercury
For each of the following, write the abbreviated configuration and list the
number of valence electrons.
5. phosphorous
6. arsenic
7. barium
8. Give the symbol and name of the element to which theses
electron configurations correspond.
a. 1s2 2s2 2p6 3s1
b. 1s2 2s2 2p3
c. 1s2 2s2 2p6 3s2 3p6 3d2 4s2
Chapter 13: Electrons in Atoms
Part 5 – Notes: Electromagnetic Radiation and Waves
Objectives: Calculate the wavelength, frequency, or speed
of a wave.
Identify, define, and explain: electromagnetic radiation, amplitude, wavelength,
frequency, hertz, spectrum, wave, crest, trough, electromagnetic spectrum,
visible spectrum, sound waves, and speed of light.
Differentiate between sound waves and radio waves.
List the parts of the electromagnetic spectrum and their relative energies.
List the components of the visible spectrum in order of frequency or wavelength.
Calculate the wavelength or frequency of a radio station signal.
Differentiate between electromagnetic waves and non-electromagnetic waves
in terms of speed and energy.
State and explain the relationship between wavelength and frequency.
Text Reference: Section 13.3 (Part) – pages 372-375
WAVES
Waves transmit energy through a medium. If you give a stone kinetic
energy (you throw it) and it lands in the middle of a pond with a smooth
surface, “ripples” will form on the surface of the water. Those “ripples”
are waves. The energy from the stone is transferred through the medium, water,
in the form of waves. If a twig is floating on the surface of the water,
the waves will move the twigs vertically (up and down) but will not carry
the twig horizontally.
Waves can be represented using drawings and mathematical equations.
The crest of a wave is the top peak of the wave. The wave’s trough
is the bottom point of the wave.
An imaginary line may be drawn horizontally at an equal distance from both
the crest and the trough of the wave. The amplitude of a wave is the
distance from the imaginary line to the crest or trough of a wave.
The frequency of a wave is the number of waves that pass a given point in
a specified unit of time.
The symbol for frequency is the Greek letter nu. Nu = ____________.
The unit for frequency is hertz, which is abbreviated
Hz. One hertz is equal to one cycle per second.
Wavelength is the distance between similar points in a set of waves, such
as from crest to crest or trough to trough.
The symbol for wavelength is the Greek letter lambda. Lambda = ____________.
The most common unit used when expressing wavelength is
meter; however, the Angstrom is also used.
Angstrom = ____________
1 Angstrom = 1 x 10-8 cm (exactly) = 1 x 10-10 m (exactly)
The speed of any wave equals wavelength times frequency. Examine how
the units define your relationship.
Formula for the speed of a wave:
Example 1: A water wave has a frequency of 4.75 x 10-2
Hz and a wavelength of 1.50 x 101 m. Calculate the wave’s speed.
Example 2: The speed of a wave is 4.75 m/s and its frequency
is 8.35 Hz. Calculate the wavelength.
ELECTROMAGNETIC RADIATION
Electromagnetic radiation is energy that can travel through a vacuum, in
the form of waves and at the speed of light. Electromagnetic radiation
has no mass.
NOTE: For the time being, whenever you are solving problems
that involve electromagnetic radiation, assume that all electromagnetic waves
travel at the speed of light even though they are not in a vacuum.
The speed of light, c, is 3.00 x 108 meters/second. The speed of any
wave is equal to the product of its wavelength and frequency. From
this information it is easy to derive that when electromagnetic waves are
concerned: speed of light = wavelength times frequency.
FORMULA:
NOTE: Whenever you are solving problems using the formula
give above, make certain that all measurements for wavelength are expressed
in meters. If the wavelength is given in Angstroms, convert Angstroms
to meters then apply the formula.
Relationship between frequency and wavelength:
For a complete diagram of the electromagnetic spectrum, see figure 13.10
on page 373 of your textbook. Note that visible light makes up a very
small portion of the whole electromagnetic spectrum.
You should recall from previous science classes that the visible light consists
of seven different colors. These colors listed in order of increasing
frequency are:
Of the parts of the visible spectrum, which has the lowest wavelength?_______________
lowest frequency? _______________
Of the parts of the visible spectrum, which has the highest wavelength?_______________
highest frequency? _______________
There are no precise boundaries between the various types of waves that compose
the electromagnetic spectrum; and there are not precise boundaries between
the various colors of visible light. However, the following frequencies
are associated with the colors indicated.
WAVE FREQUENCY
Red light 4.3 x 1014 Hz
Yellow light 5.2 x 1014 Hz
Blue light 6.4 x 1014 Hz
Violet light 7.5 x 1014 Hz
Radio Waves
Radio stations send out radio waves on a specific frequency. Depending
on the strength of the broadcasting antenna, the listening area may be large
or small. No two broadcasting signals may be the same in overlapping
areas.
For AM radio stations, the station call number is the
frequency of the radio wave in kilohertz, kHz (x 103Hz). The frequencies
range from 53 to 170 on the AM band. For FM radio stations, the station
call number is the frequency of the radio wave in megahertz, MHz (x 106 Hz).
The frequencies go from 88 to 108 on the FM band. These individual
frequencies have associated wavelengths that may be determined through calculations.
Example 1: A gamma ray has a frequency of 3.75 x 1023 Hz.
What is the wavelength?
Example 2: What radio station sends out a signal with a
wavelength of 3.25 m?
Chapter 13: Electrons in Atoms
Part 5 – Assignment: Electromagnetic Radiation and Waves
Answer the following questions, neatly and completely. Show all set-ups,
work, units, etc.
1. The speed of sound at 15.0oC is 340. m/s. What
is the wavelength of a sound wave with a frequency of 27.5 Hz?
2. A stone is tossed into a pond. The kinetic energy
of the stone is transferred to the water and produces a wave. A cork
floating in the water floats up and down at a rate of 15.0 times in 5.00
seconds. What is the frequency of the wave produced in hertz?
3. Calculate the wavelength of the waves produced by the
stone from question 2 in Angstroms. (Use the answer from #2.)
4. List the colors of the visible spectrum in order of
increasing frequency?
5. What radio station sends a signal with a wavelength
of 3.007 m?
6. What is the wavelength of the signal sent from the antenna
of WDHA (105.5 FM)?
7. What is the wavelength of the signal sent from the antenna
of 770. AM?
8. A beam of infrared light has a frequency of 5.469 x
1013 Hz. What is the wavelength?
9. A hydrogen lamp emits several lines in the visible region
of the spectrum. One of these lines has a wavelength of 6.56x10-5 cm.
What are the color and frequency of this radiation?
10. A mercury lamp emits radiation with a wavelength of
4.36x10-7 m.
a. What is the wavelength of this radiation
in centimeters? in Angstroms?
b. In what region of the electromagnetic
spectrum is this radiation?
c. Calculate the frequency of this radiation.
Chapter 13 – Electrons in Atoms
Part 6 – Notes: Energy, Photons, Bright-Line Spectrum, and the Photoelectric
Effect
Objectives: Calculate the wavelength, frequency, or energy
of light.
Explain the origins of the atomic emission
spectrum of an element.
State and explain the relationship
between energy and wavelength and between energy and frequency.
Differentiate between ground and excited states and explain how it is easier
to remove an electron from a higher energy level.
Identify, define, and explain: spectrum, atomic emission spectrum, Planck’s
constant, photons, photoelectric effect, ground state, de Broglie equation,
and Heisenberg uncertainty principle.
Text Reference: Section 13.3 – pages 374-382
The Bright-Line Spectrum
∑ You are aware that every frequency in the electromagnetic spectrum is associated
with a specific quantum energy.
∑ When electromagnetic energy is put through a light bulb, the light bulb
releases photons with energies associated with all of the frequencies from
red to violet light. The combination of all the frequencies from red
to violet produces white light. When the white light is observed through
a prism, a continuous “rainbow” of colors appears to the observer.
∑ Atoms of a gas can be excited by passing electricity through a gas contained
inside a glass tube.
Expectation:
Reality:
Why:
Ground State:
Excited States:
You are familiar with the fact that electromagnetic radiation displays characteristics
of both waves and particles: the wave-particle duality. Electromagnetic
radiation is transferred to matter in units or quanta of energy called PHOTONS.
The energy of a photon is directly proportional to the frequency of electromagnetic
radiation. So, as the frequency of an electromagnetic waves increases,
the energy of the photons from that wave will also increase.
Each frequency has a specific energy. The relationship between energy
of a photon and frequency can be expressed by the following mathematical
relationship.
Energy
of a photon = Planck’s constant x frequency
or
Formula:
The symbol for energy is E.
You should already know the unit for energy is joule and is abbreviated _______.
A joule is _________________________.
You know that the symbol for frequency is __________ with units of ________________________________________.
The symbol for Planck’s Constant is _______________. Planck’s Constant
is equal to ______________________________.
The speed and energy equations may be combined into de Broglie’s Equation:
Relationships:
What type of relationship exists between frequency and
wavelength?
What type of relationship exists between frequency and
energy of a photon?
What type of relationship exists between wavelength and
energy of a photon?
Laws of classical physics – there is no limit to how large or how small the
energy gained or lost by an object may be.
So according to this, the bright-line spectrum should
be a continuous rainbow. But it is NOT.
We cannot always apply macroscopic laws to subatomic events.
Max Planck – German physicist – 1858-1947
Question: Why does an object change color when heated? Heating iron
causes it to change from black to yellow to red to white to blue as its temperature
is increased.
Answer: The energy of a body changes only in small discrete units –
quanta – small packages of energy.
Page 376 – It appears that thermal energy may continuously supplied to heat
liquid water to any temperature between 0o and 100oC. Actually the
water temperature increases by infinitesimally small steps, which occurs
as individual water molecules absorb quanta of energy. An ordinary
thermometer is unable to detect small changes in temperature. Thus
your everyday experiences give you no clue to the fact that energy is quantized.
Remember, the energy of a photon of light, heat, or other radiation is calculated
by E = hv.
The Photoelectric Effect
∑ When light shines on metals they emit electrons (more specifically called
photoelectrons). The alkali metals are particularly sensitive to the
effect.
∑ The light has to have a high enough frequency – in other words have enough
energy.
∑ Potassium
o Red light – v = 4.3x1014 Hz to 4.6x1014Hz – will not cause an electron
to eject from potassium – no matter how much of the light gets used.
o Yellow light – v = 5.1x1014Hz to 5.2x1014Hz – will start the process of
ejecting electrons from potassium – even if it is very weak in intensity.
∑ Not enough energy – no photoelectrons ejected
∑ Just above threshold energy – electron ejected with minimal energy/speed
∑ Well above threshold energy – electron ejected with significant energy/speed
∑ Greater intensity of light – more waves of a given frequency – more electrons
ejected
∑ The number of electrons ejected depends on the number of light waves –
the intensity.
∑ The energy of the ejected electrons depends on the frequency (or energy)
of the light waves.
Heisenberg Uncertainty Principle
It is impossible to know both the position and the velocity of a particle
at the same time. The more you find out about one of the pieces of
information, the less you are able to determine about the other. You
need to use information about the position at an instant to find information
about its speed – but by the time you look at that position, it is already
gone and you know nothing about its new position – unless you use information
about its speed – but then you will not know anything about its new velocity.
This uncertainty is more obvious and significant with
small objects than with large objects. Comparing an electron and a
baseball – there is the uncertainty with the baseball – but it is so small
it is nearly immeasurable. But, with regard to an electron, the uncertainty
is much more significant due to the extremely small size of an electron.
Chapter 13 – Electrons in Atoms
Part 6 – Assignment: Energy, Photons, Bright-Line Spectrum, and the Photoelectric
Effect
Solve the following problems. Show all set-ups, work, units, etc.
Solve problems 1 – 6 on a separate sheet of paper.
1. A photon from a source of electromagnetic radiation
transmits 4.58 x 10-19 J of energy to matter. What is the frequency
of this electromagnetic radiation? What is the wavelength of the electromagnetic
radiation?
2. What is the wavelength of electromagnetic radiation
if a photon transmits 2.04 x 10-18 J of energy to matter?
3. Calculate the quantum energy from the electromagnetic
radiation with a frequency of 3.20 x 1021 Hz.
4. Calculate the quantum energy from electromagnetic radiation
with a wavelength of 4.20 x 10-7 m.
5. What is the energy of the radio wave from station WKTU
– 92.3 FM?
6. A radio wave has a wavelength of 2.921 m. What
is the energy of the radio station signal?
7. Electromagnetic radiation exhibits properties of both
__________________ & __________________.
8. A “packet” or “unit” of electromagnetic radiation is
called a ____________________.
9. Different __________________ of light carry different
amounts of energy per photon.
10. An atom that possess excess energy is said to be in
a(n) ____________________ state.
11. An atom may release its excess energy by emitting a(n)
____________________ of electromagnetic energy.
12. A beam of red light has higher
or lower energy photons than blue light.
(Choose one.)
13. Because a given element’s atom emit only certain photons
of light, we know only certain _______________ _______________ are occurring
in those particular atoms.
14. The energy of an emitted photon corresponds to the
difference in energy between the different ____________ _______________ of
the atom.
15. How do we know that the energy levels of the hydrogen
are not continuous, as physicists originally assumed?
16. Explain the origin of the atomic emission spectrum
of an element.
17. Can classical physics explain the photoelectric effect?
Explain.
18. Compare the ground state and the excited state of an
electron.
19. What will happen if the following occur?
a. Monochromatic light shining on the
alkali metal cesium is just above the threshold frequency.
b. The intensity of light increases
but the frequency remains the same.
c. Monochromatic light of a shorter
wavelength is used.
20. What will happen when a hydrogen atom absorbs a quantum
of energy?
Chapter 13 – Electrons in Atoms
Part 7 - Notes: Quantum Numbers
Objectives: Identify, define, and explain: quantum number,
principal quantum number, angular momentum quantum number, magnetic quantum
number, and spin quantum number.
Use three quantum numbers to identify a given atomic orbital
and four quantum numbers to identify an electron.
Explain why no two electrons in a given atom can have
the same four quantum numbers.
Give a brief description of what each of the four quantum
numbers does and how it functions to denote a portion of an electron’s address
in an atom.
Text Reference: Page 364
Scientists have been unable to determine the exact position of an electron
in an atom. Electrons in an atom may move to higher or lower energy
levels by absorbing or releasing energy, in units or quanta of energy.
Also, electrons at different energy levels are believed to travel in certain
regions called orbitals. These orbitals are a probability map for the
location of an electron.
The exact location of an electron cannot be pinpointed; however, the electron
may be described using quantum numbers. There are four quantum numbers.
The numbers represent an electron’s address within an atom. No two
electrons in the same atom can have the same address at the same time.
The Principal Quantum Number = n
The first quantum number is called the principal quantum number. It
describes the energy level of an electron. The size of orbitals increases
as the energy level increases; so it may be said that the first quantum number
is related to the size of the orbital. The letter n is the abbreviation
for the principal quantum number.
Energy levels range from n = 1 to n = infinity. The value of n must
be a whole number from one to infinity.
The Angular Momentum Quantum Number = l
The second quantum number is called the angular momentum quantum number and
it describes the shape of the orbital in which the electron has the highest
probability of being found. The letter l is the abbreviation for the
angular momentum quantum number.
Orbitals may have the shape of a sphere. Sphere-shaped orbitals are
called s-orbitals and are designated by a numerical value of l = 0.
Orbitals may have two-lobe shapes and be called p-orbitals. P-orbitals
are designated by a numerical value of l = 1. There are also “four-lobed”
orbitals called d-orbitals. These orbitals are designated numerically
by l = 2. There are more complex orbitals with unusual shaped called
f-orbitals. F-orbitals have a numerical designation of l = 3.
Other orbitals theoretically exist and are designated by numbers l = 4, 5,
6, …, to a maximum value of n – 1.
So, when an electron has a principal quantum number of n, it may have an
angular momentum quantum number that is any whole number from 0 through n
– 1.
The Magnetic Quantum Number = m
The third quantum number is called the magnetic quantum number and it describes
the orientation of the orbitals around the x, y, or z-axis. The abbreviation
for the magnetic quantum number is m. Values of m range from –l to
+l and all whole number integers in between.
The first three quantum numbers make up 3/4 of an electron’s address but
they also define the orbital in which the electron has the greatest probability
of being found. No two orbitals can have the same first three quantum
numbers otherwise it allows for two orbitals to be in the same space and
that can’t happen.
Spin Quantum Number = ms
The fourth quantum number is called the spin quantum number and it indicates
the spin of the electron being described. The fourth quantum number
is abbreviated ms.
Electrons are believed to spin about their own axes. When two electrons
occupy the same orbital they are said to spin in opposite directions.
By convention, one electron is arbitrarily assigned a spin of +1/2 and the
other is assigned a spin of –1/2.
NOTE: The energy of an electron is defined by its four quantum numbers.
No two electrons in the same atom may have the same set of four quantum numbers
at the same time. This is the Pauli Exclusion Principle. It basically
says that no two electrons can be in the same space at the same time.
Chapter 13 – Electrons in Atoms
Part 7 - Assignment: Quantum Numbers
1. TRUE or FALSE: Scientists are
able to determine the exact position of electrons in atoms.
2. An electron moves to a higher energy level by _____________
energy and to a lower level by _____________ energy.
3. Energy released by electrons is released in the form
of __________________.
4. An electron’s “address” is described by using ________________
_______________.
5. The energy level of an electron is denoted by the ____________________
quantum number.
6. The spin of an electron is denoted by the ____________________
quantum number.
7. The orientation of the orbital is denoted by the ____________________
quantum number.
8. The shape of the orbital is denoted by the ____________________
quantum number.
9. State what the following letters represent:
a. p ______________________________
b. m ______________________________
c. s ______________________________
d. ms ______________________________
e. y ______________________________
f. n ______________________________
g. d ______________________________
h. l ______________________________
i. f ______________________________
10. An electron may spin two ways. Each direction
is arbitrarily assigned a spin of __________ or __________.
11. An orbital may be defined using __________ of the hour
quantum numbers. They are _________________.
12. TRUE or FALSE: Two electrons
in an atom may have the same four quantum numbers.
13. You know the answer to number 12 because of the _______________
_______________ _______________.
14. Two electrons in an atom can have the same __________,
__________, and __________ values. It means that they are in the same
orbital.