This document provides a summary of key concepts about electrons in atoms, including: 1) It discusses the evolution of atomic models from Rutherford to Bohr, focusing on explaining the arrangement of electrons. The quantum mechanical model describes electron probability clouds rather than fixed orbits. 2) It covers atomic orbitals and how electrons fill different orbitals based on their principal and angular momentum quantum numbers. Higher principal quantum numbers correspond to higher energy levels further from the nucleus. 3) The document emphasizes that electrons fill orbitals based on the Aufbau principle to achieve the lowest possible energy configuration. Understanding electron configurations is essential to describing elements and their properties.

1. Chapter 4: Electrons in Atoms
This chapter is about electrons in the atom- a tricky
subject at best- and the evolution of the atomic model.
This chapter covers much material, some of it very
difficult and abstract. It is essential that you bring your
book to class and do all assigned homework.

2. Chapter 4: Arrangement of
Electrons in Atoms
• Atomic Models:
- already discussed atomic structure –
what was it?
- inadequate – describes only a few
properties of atoms
- need a model that is focused on
arrangement of ____, the basis of
chemistry

3. Rutherford Model of the Atom
The Rutherford Model (aka the Planetary Model) was an
improvement over the previous models, but it was still
incomplete. It did not include the distribution of the negatively
charged electrons in the atom.
We know that negative and positive particles (that is e-
and p+
)
attract each other, so the big question became:
Why don’t the electrons crash into the nucleus?

4. If + and – charges attract, why don’t e-
collapse into the nucleus?
In 1913, a student of Rutherford’s created a new model
for the atom; he proposed the e-
’s were arranged in
concentric circles around the nucleus (patterned after
the movement of planets around the sun):
The Planetary Model
Along with this, he stated that the e-
’s have fixed energy
that allows them to avoid falling into the nucleus,
analogous to the rungs of a ladder. More on this later.

5. The Planetary Model of the Atom

6. But first, let’s talk about:
The Properties of Light
Before 1900, scientists thought light behaved solely as a wave.
What idiots! It was soon discovered that light also has particle
characteristics. But let’s first review the wavelike properties.
The Electromagnetic Spectrum

7. The electromagnetic spectrum shows all the types of
electromagnetic radiation- a form of energy that exhibits wavelike
behavior as it travels through space.
All forms of electromagnetic radiation move at a constant speed
of 3.00 x 108
m/s through a vacuum. This is about 186,000 miles/s.
Also known as the speed of light.

8. Let’s talk about waves and wave motion for a minute:
Frequency and wavelength are mathematically related. This relationship is:
c = λv

9. c = λv
In the equation, c is the speed of light (in m/s), λ is the wavelength of
the electromagnetic wave (in m), and v is the frequency of the
electromagnetic wave (in s-1
or Hz).
Important: λ and v are inversely proportional, so as the wavelength
of light increases, the frequency decreases and vice versa.
Practice Problems
1. Determine the frequency of light whose wavelength is 4.257 x 10-5
m.
2. Determine the wavelength (λ) of a photon whose frequency is 3.55 x 1017
s-1
.

10. Electromagnetic Spectrum

11. The Photoelectric Effect
The photoelectric effect is a phenomenon that refers to:
the emission of electrons from a metal when light shines
on the metal.
You’re most likely thinking: who cares?
Well, here’s the thing- for any given metal, no electrons were
emitted if the light’s frequency were below a certain minimum.
Metal
Light
Electrons

12. The Photoelectric Effect (cont’d)
So, obviously, light was known to be a form of energy, capable of
knocking electrons loose from metal. But (important):
the wave theory of light predicted that any frequency of light could
supply enough energy to eject an electron, so the fact that there had
to be a minimum frequency for a given metal made no sense.
Something about the assumption of light behavior was wrong.
Metal
Light
Electrons

13. The Particle Description of Light
The German physicist Max Planck came up with the idea that light
is emitted in small packets called quanta.
A quantum of energy is the minimum quantity of energy that
can be gained or lost by an atom.
Here is the relationship between quantum and frequency of radiation:
E = hv
Where E is the energy (J), v is the frequency (s-1
), and h is the
physical constant called Planck’s Constant; h = 6.626 x 10-34
J·s
S’up.

14. The Particle Description of Light
In 1905, Einstein took this idea further by stating that light can
act as both a wave and a stream of particles. Each particle of light
carries a quantum of energy and is called a photon.
A photon is a particle of electromagnetic radiation having zero
mass and carrying a quantum of energy.
Ephoton = hv
Einstein was able to explain the photoelectric effect this way.
Different metals bind their electrons differently, so v changes.

15. The Hydrogen-Atom Line-Emission Spectrum
When an electric current is passed through a gas sample at low
pressure, the potential energy of the gas changes.
The ground state of an electron, the energy level it normally
occupies, is the state of lowest energy for that electron.
There is also a maximum energy that each electron
can have and still be part of its atom. Beyond that
energy, the electron is no longer bound to the nucleus of
the atom and it is considered to be ionized.
When an electron temporarily occupies an energy state
greater than its ground state, it is in an excited state. An
electron can become excited if it is given extra energy,
such as if it absorbs a photon, or packet of light, or
collides with a nearby atom or particle.

16. The Hydrogen-Atom Line-Emission Spectrum
So what does this mean?
Well, when scientists passed an electric current through a vacuum
tube with a pure gas in it (like H or O), each atom would go through
the steps listed above: they would gain energy, and then reemit it
in the form of a photon or light. This light was then passed through
a prism, and the wavelengths (colors) in that element could be seen.
Electrons do not stay in excited states
for very long – they soon return to their
ground states, emitting a photon with the
same energy as the one that was absorbed.

17. The Hydrogen-Atom Line-Emission Spectrum
So let’s use the example of helium. A tube of helium has a current of electricity
pass through it, and the absorbed energy is then released in the form of light, thus,
the tube glows. That light is then passed through a prism, which separates all the
colors (wavelengths) in that light. Helium has a particular emission-spectra, or set
of lines at specific color spectra.
Every element has a signature color spectra.

18. The Hydrogen-Atom Line-Emission Spectrum
But why are there only some colors appearing and
not all of them?
Because the electrons in these atoms have specific
fixed energy levels, and only give off certain colors
when jumping from level to level. Whenever an
excited helium atom falls to its ground state or to a
lower-energy excited state, it emits a photon of
radiation. The energy of this photon (Ephoton = hv) is
equal to the difference in energy between the atom’s initial state and
it’s final state. Because different atoms have different energy levels,
different atoms give off different frequencies (colors) of light.

19. The Bohr Model of the Hydrogen Atom
Niels Bohr, scientist extraordinaire, solved the puzzle of why
different atoms give off different color spectra. He linked the
atom’s electrons to photon (color spectra) emission. According to
his new model, electrons can only circle the nucleus in allowed
paths, or orbits.Notice this!

20. The Bohr Model of the Hydrogen Atom (cont’d)
When energy is added to an atom, the electrons move up energy level(s).
Conversely, when energy is given off by an atom (in the form of a photon),
the electrons move down one or more energy levels.
The principal quantum number is
denoted with the letter n, and it
indicates the main energy level
occupied by the electron. As n
increases, the electron’s energy and
it’s average distance from the nucleus
increases.

21. Plotting the Electron “Orbit”
It would be inaccurate to say that the electrons orbit the nucleus in
the same way the planets orbit the sun, i.e., in a fixed and set path.
The Heisenberg Uncertainty Principle states that you can know
the position and velocity of an electrons at any given point, but
never both at the same time. So if you were to plot the position of
an electron many, many times, you would begin to build a picture
of where it occupies space 90% of the time. This is called an
orbital.

22. Plotting the Electron “Orbit”
Orbital: the probable location of an electron around the nucleus.
As n increases, the number of different types of orbitals increases as
well. At n = 1, there is one type of orbital; at n = 2, there are two
types of orbitals; and so on. The number of orbitals at any given
energy level is equal to the principal quantum number (n). These
are known as sublevels.

23. Types of Orbitals
1. s-orbitals: s-orbitals are spherical in shape, representing a hollow
ball where you can find the electron 95% of the time. They are
labeled 1-s, 2-s and so on to denote how close they are to the
nucleus.

24. Types of Orbitals (cont’d)
2. p-orbitals: At the 1st
energy level, the only orbital available to the
electrons is the s-orbital. But at the 2nd
energy level- after the 2-s
orbital- there is the 2-p orbital. The p-orbitals are dumbbell shaped
to represent where the electron can be found 95% of the time.
Notice that near the nucleus, the area where they are usually found
is very narrow.

25. Types of Orbitals (cont’d)
2. p-orbitals (cont’d): unlike s-orbitals, p-orbitals point in a particular
direction. At any one energy level it is possible to have three
absolutely equivalent p orbitals pointing mutually at right angles
to
each other. These are arbitrarily given the symbols px, py and pz.
This is simply for convenience - what you might think of as the x,
y or z direction changes constantly as the atom tumbles in space.

26. Types of Orbitals (cont’d)
3. d-orbitals: after the s and p orbitals, there is another set of orbitals
which becomes available for electrons to inhabit at higher energy
levels. At the third level, there is a set of five d orbitals (with more
complex shapes names) as well as the 3s and 3p orbitals (3px, 3py,
3pz). At the third level there are a total of nine orbitals altogether.
3dxy
3dxz
3dyz
3dx
2
-y
2
3dz
2

27. N
“Rungs of a ladder”
Energy of e-
increases as you
travel further
away from the
nucleus.
e- can jump
from energy
levels when
they gain/lose
energy
Quantum = amount of energy req’d to move an e-
from its present energy level to the next highest;
“quantum leap”
Unlike a ladder,
levels are not
evenly spaced;
closer further
away thus
easier to move
b/t or leave.

28. The Quantum Mechanical Model
(QMM)
• This is the most modern description of e-
in
an atom; it is purely mathematical and
describes the _____ and _____ of an e-
.
• All previous models differed b/c they were
_______.
• This model doesn’t define an exact path of
an e-, rather the QMM does what?
“Chance”

29. • QMM = probability of finding an e- within
a certain volume surrounding the nucleus;
represented by an electron cloud
The > probability
of finding an e- is
within these
areas
surrounding the
nucleus
(represent where
the e- is 90% of
the time).
N
The “fatter” the
area of the e-
cloud, the greater
the chance of
finding an e- and
vice versa.

30. Atomic Orbitals
• Designate energy levels that e-
are in by using principal
quantum numbers (n)
• n is ordered from lowest 
highest energy level
(1,2,3,4…); thus the higher the
principal quantum # the further
the e-
is from the nucleus.
• i.e.) an e-
in the 3rd
principal
energy level has more ___ and
is further from the ___ than an
e-
in the 2nd
principal energy
level.
n =1
n = 2
n = 3
n = 4
↑energy,↑distancefrom
nucleus,↓spacing
N

31. • Within each energy
level there are
sublevels; the # of
sublevels equals the
principal energy level
(n)
• The sublevels are also
arranged from lowest to
highest energy
• These sublevels have
orbitals within them;
each orbital can hold a
max of 2 e-
Principal energy
level (n)
# of sublevels in
that level
n = 1 1 sublevel
n = 2 2 sublevels
n = 3 3 sublevels
Sublevels
(lowest
highest energy)
# of orbitals
within each
sublevel
1st
= s 1 orbital
2nd
= p 3 orbitals
3rd
= d 5 orbitals
4th
= f 7 orbitals

32. Do Now:
1. Discuss points you have learned about the PT:
a. What does it tell us?
b. How can we use it to talk about an element
and its characteristics?
c. How and why do we use the Aufbau
Diagram?
Homework:
1. Finish electron configuration sheet; QUIZ
2. Bring all lab materials tomorrow…

33. Basically…
Principal energy level (n)  Energy sublevels  Orbitals in sublevels
n = 1, 2, 3, 4… s, p, d, f, g… s =1; p = 3; d = 5; f = 7
(2 e-; 6 e-; 10 e-; 14 e-)
QMM describes an e-
position within an e-
probability cloud; e-
don’t
travel in fixed circular paths, therefore we cannot call them orbits.
Rather, we call them atomic orbitals (s, p, d, f, g…)  SHAPES OF
ATOMIC ORBITALS DICTATE PROBABILITY!!!
s orbital
p orbital (x 3)
d orbital (perpendicular
orbital coming at you; x 5)
Fig 13.4, 5 in
book
Low to High

35. Another representation of the
atomic orbitals…
Clouds/”bubbles” indicate where you’ll find e- most of the
time!

36. • Notice w/ p and d orbitals the regions
close to the nucleus where probability of
finding an e- is very narrow = node
• Again, the # and types of atomic orbitals
depends on what?
• Example: lowest principle energy level is
n = 1; it has 1 atomic orbital called 1s
Does the probability of finding an
e- vary with direction in 1s? Does
the same hold true for p and d
orbitals?

37. • The 2nd
energy level (n = 2) has 2
sublevels, s and p.
N PP
P
P
P
Coming @
you
Going away
from you
3.) Spaces
represent
what?
P
S
2.) How many total
orbitals are there?
What are the max # of
e- that can be held in
n= 2?
1.) P orbitals
stick out
further
therefore they
have > ____?

38. • The 3rd
principal energy level (n = 3) has how
many orbitals? Can you name them? What is
the max # of e- this energy level can hold?
• The 4th
principal energy level (n = 4) has how
many orbitals? Can you name them? What is
the max # of e- this energy level can hold?

39. • As mentioned, the principal quantum # always
equals the # of sublevels in that energy level
• The max # of e- that can occupy a principal
energy level is given by the formula…
2n2
What is the max # of e- in the 6th
principal energy
level? Sublevels?
Still confused? Review p. 366 for max e- per
energy level

40. Homework
• Electron configuration worksheet (work
on wkst.)
• Have homework out to go over…
• Do Now:
1. What is the Aufbau Diagram? How do
you create it? What does it tell about
filling orbitals? (use book to help you out)
2. What is the total # of e- in n = 9? n = 5?
3. What does the quantum # tell you?

41. Electron Configurations
• Natural phenomena to work towards
stability – lowest possible energy
WHY?
High energy systems are
very unstable
Atom works to attain the most stable e-
configuration possible

42. • There are 3 rules that help you to
determine this:
1. Aufbau Principle
2. Pauli Exclusion Principle
3. Hund’s Rule
1 s 2 s 2 p
Long form vs. Short
form?
Electron Configurations/Aufbau Diagrams

43. 1) Aufbau principle: Electrons enter orbitals of lowest energy first.
The various sublevels of a principle energy level are always of
equal energy. Furthermore, within a principle energy level the s
sublevel is always the lowest-energy sublevel. Each box represents
an atomic orbital.
Aufbau Diagram

44. 2) Pauli exclusion principle: An atomic orbital may describe at most
two electrons. For example, either one or two electrons may occupy
an s orbital or p orbital. A vertical arrow represents an electron and
its direction of spin (↑ or ↓). An orbital containing paired electrons
is written as ↑↓ .
3) Hund’s Rule: When electrons occupy orbitals of equal energy, one
electron enters each orbital until all the orbitals contain one
electron with parallel spins. For example, three electrons would
occupy three orbitals of equal energy as follows: ↑ ↑ ↑
Second electrons then add to each orbital so their spins are paired
with the first electrons.

45. Some practice:
____
5s ___ ___ ___
4p
___ ___ ___
4d
___ ___
Element

46. Electron Configuration
This is the order which electrons will fill their energy levels:
You MUST learn this!

47. Electron Configuration (cont’d)

48. Noble Gas Configurations
A much easier way to write electron configurations, abbreviates all the orbital
notation. This is an acceptable way to write electron configurations on quizzes or
tests.

49. Show the electron configuration of the following elements:
1) Fe: 1s2
2s2
2p6
3s2
3p6
4s2
3d6
2) Ga: 1s2
2s2
2p6
3s2
3p6
4s2
3d10
4p1
3) Ar: 1s2
2s2
2p6
3s2
3p6
4) Sr: 1s2
2s2
2p6
3s2
3p6
4s2
3d10
4p6
5s2
5) Mg: 1s2
2s2
2p6
3s2
6) Ru: 1s2
2s2
2p6
3s2
3p6
4s2
3d10
4p6
5s2
4d6

50. Homework
• Have worksheets out to quickly review
questions (13.1 and 2)
• Complete 13.3, #1,2, 4, 6 (on loose-leaf,
neatly, showing equations used, all work and
cancellations in a vertical fashion); will go
over next session; use p. 375 example to help
• Do Now:
1. Starting form n = 1 (to n = 4), list the order that
electrons would fill sublevels…
2. Quickly list and discuss all three rules for e-
configuration discussed previously…

51. Take Quiz – 7 minutes
Do Now:
1. What is the difference between an atom and its
ion?
2. What is a node?
3. Why is it unnatural for systems/atoms to be at
high energy? How do atoms fix this problem?
Homework –
Complete chapter 13 worksheet (1st
page, front
and back on the worksheet)

52. Physics and the QMM
• QMM developed through study of light
• Through its study, found light was energy
that contained _____ and moved by ____.

53. • According to the “wave model”, light
consists of electromagnetic waves
• Includes…
All waves travel
in a vacuum at
3.0 x 10^10 cm/s
(or 3.0 x 10^8
m/s)  = ?
I’m
smarter
than he is?
How’d he
measure
that?

54. Anatomy of a Wavelength
origin
amplitude
Λ = “lambda”
Frequency (ν) = “nu”
= # of wave cycles that
that pass through a
point in a given time
= Hertz (Hz) or s^-1
Wavelength and
frequency are
inversely related!
Which leads us
to…

55. Take 3 minutes only for quiz – hand
in when finished.
Do Now:
1. Give the basic anatomy of a wavelength.
2. What do we broad term describes all forms of light?
Which portion makes up the smallest portion of this
“spectrum”?
3. How are wavelength and frequency related? Do they
relate to anything else?
4. Have essays and homework questions ready!
Homework:
1. Massive quiz on Monday (in lab) on all ch. 13
2. Remember to bring notebooks to class.
3. Tuesday – Print out a PT and after reading chapter 14,
create a “map” of how to interpret the periodic trends

56. ν “times” λ = speed of light
• Every time!
• Light bends through prisms to create the…
Electromagnetic Spectrum =
relative size?

57. Every element bends light in a
specific way…
Open book and complete sample 13.2 and
practice problem 11

58. Another idea that came about
through the study of light…
• The color change associated with the
heating/cooling of an object occurs through the
+/- of energy units = “bricks of a wall”
• Large energy change = emission/abs. of high
frequency radiation and vice versa… thus,
frequency and Planck’s constant are?
E (“radiant energy”)= frequency x Planck’s
constant
• E = ?
• Problem 13 on page 379