1. ? AP Chemistry Electronic Structure of Atoms
electronic structure: the arrangement of
electrons in an atom
quantum mechanics: the physics that correctly
describes atoms ?

2. electromagnetic radiation (i.e., light)--
waves of oscillating electric (E)
and magnetic (B) fields --
source is… vibrating electric charges E B

3. Characteristics of a Wave
crest
amplitude A
trough
wavelength l
frequency: the number of cycles per
unit time (usually sec)
-- unit is Hz, or s–1

4. electromagnetic spectrum: contains all of the “types” of
light that vary according to frequency and wavelength IR UV
visible
X-rays
radio waves
microwaves
gamma rays
cosmic rays
ROYGBV
750 nm
400 nm
large l
small l
-- visible spectrum ranges from
only ~400 to 750 nm (a very
narrow band of spectrum)
low f
high f
low energy
high energy

5. first to get an accurate value for speed of light
Albert Michelson (1879) --
first to get an accurate
value for speed of light
Albert Michelson
(1852–1931)
The speed of light in
a vacuum (and in air)
is constant:
c = 3.00 x 108 m/s
-- Equation:
c = n l = f l

6. that energy can be absorbed or released only in certain
In 1900, Max Planck assumed
that energy can be absorbed
or released only in certain
discrete amounts, which he
called quanta.
Later, Albert Einstein dubbed
a light “particle” that carried a
quantum of energy a photon.
Max Planck
(1858–1947)
-- Equation:
E = h n = h f
E = energy,
in J
h = Planck’s constant
Albert Einstein
= 6.63 x 10–34 J-s (i.e., J/Hz)
(1879–1955)

7. A radio station transmits
at 95.5 MHz (FM 95.5).
Calculate the wavelength
of this light and the energy
of one of its photons.
3.00 x 108 m/s =
95.5 x 106 Hz
c = f l
= m
E = h f
= x 10–34 J/Hz (95.5 x 106 Hz)
= x 10–26 J

8. In 1905, Einstein explained the photoelectric effect
using Planck’s quantum idea.
-- only light at or above a threshold freq. will
cause e– to be ejected from a metal surface
ROYGBV e–
light source
metal surface e–
Frequency (i.e., energy)
of light determines IF e–
are ejected or not, and
with what KE. e–
Intensity/brightness of
light determines
HOW MANY e– are
ejected.

9. ? Einstein also expanded Planck’s idea, saying that
energy exists only in quanta.
Light has both wavelike and particle-like qualities,
and...
so does matter. ?

10. “continuous” spectrum.
Line Spectra
Ordinary white light
is dispersed by a
prism into a...
“continuous” spectrum.
From the gas in a nearly-evacuated gas-discharge
tube, we instead get a...
line spectrum.
H2 absorption spectrum
H2 emission spectrum
(if the H2 is absorbing
light from an
external source)
(if the H2 has been
energized and is
emitting light)

11. Niels Bohr took Planck’s quantum idea and applied
it to the e– in atoms. --
e– could have only
certain amounts of
energy --
e– could be only at
certain distances from
nucleus
Niels Bohr
(1885–1962)
e– found
here
e– never
found here
planetary
(Bohr) model N

12. -- Bohr assumed that the e– in his circular orbits
had particular energies, given by:
RH = Rydberg constant
= 2.18 x 10–18 J
n = 1, 2, 3, ... (the principal
quantum number)
The more/less (–) an
electron’s energy is...
i.e., the energy level
the more/less stable the atom is.
“barely”
(if at all)
stable
When n is very large, En
goes to zero, which is the
most energy an e– can have
because…
“barely” (–) E
energy “well” e– e–
“a bit”
stable
zero is larger
than anything (–).
“a bit” (–) E
(e– has
escaped completely from atom.) e–
very (–) E
very stable

13. -- Bohr stated that e– could move from one level to
another, absorbing light of a particular freq. to
“jump up” and releasing light of a particular freq.
to “fall down.”
He: 1s1 2s1
He: 1s2
EMITTED LIGHT
ENERGY
(HEAT, LIGHT,
ELEC., ETC.)
-- Bohr’s model (i.e., its specific equation) worked
only for atoms with… a single e–.

14. Find the wavelength, frequency,
and energy of a photon of the
emission line produced when an
e– in a hydrogen atom makes the
transition from n = 5 to n = 2.
For n = 5…
= –8.72 x 10–20 J
For n = 2…
E2 = –5.45 x 10–19 J
DE = 4.58 x 10–19 J
= energy of photon
E = h f
= x 1014 Hz
c = f l
= x 10–7 m

15. The Wave Behavior of Matter
Since light (traditionally thought of
as a wave) was found to behave as
both a wave and a particle, Louis de
Broglie suggested that matter
(traditionally thought of as particles)
might also behave like both a wave
and a particle. He called these…
matter waves.
Louis de Broglie
(1892–1987)
-- The wavelength of a moving
sample of matter is given by:
m = mass
(kg)
v = speed
(m/s)

16. A proton moving at 1200 m/s would be associated with a matter wave
of how many nanometers?
In the absence of further info…
mp ~ 1 amu
= 1.66 x 10–27 kg
(actual p+ mass
is ~1.673 x 10–27 kg)
= 3.3 x 10–10 m
= nm

17. A wave is smeared out through space, i.e., its location
is not precisely defined. Since matter exhibits wave
characteristics, there are limits to how precisely we
can define a particle’s (e.g., an e–’s) location.
-- the limitation also applies to a particle’s...
momentum
-- Heisenberg’s uncertainty principle:
It is impossible to know simultaneously
BOTH the exact momentum of a particle
AND its exact location in space.
D = “uncertainty in”
h = Planck’s const.
Werner Heisenberg
(It is inappropriate to imagine an e– as a solid particle moving in a well-defined orbit.)
(1901–1976)

18. Schrodinger’s wave equation (1926) accounts for
both wave and particle behaviors of e–.
(for a non-relativistic particle of mass m w/no electric charge and zero spin,
where h-bar is the reduced Planck’s constant (=h/2p),
V is the potential energy, and Y is the wave function)
-- Solutions to the wave equation
yield wave functions, symbolized
by Y, which have no physical
meaning, but Y2 at any point in
space gives the probability that
you’ll find an e– at that point. Y2
is called the probability density,
which gives the electron density.
Erwin Schrodinger
(1887–1961)

19. -- Orbitals describe a specific distribution of electron
density in space.
Each orbital has a characteristic shape and energy.

20. (“Not.”)
(Well, theory says that there ARE g orbitals, but they don’t look like this.)
We also think g orbitals exist, and they look like this…
The lanthanides and actinides contain f orbitals.

21. Quantum numbers are used to describe where an e–
is in an atom.
1. principal quantum number, n
(n = integers 1, 2, 3,...)
-- correspond to the energy level of the electrons
-- All orbitals having the same n are called an
electron shell (e.g., 2s and 2p).
2. angular momentum quantum number, l
(l = integers from 0 up to (n – 1))
-- This number defines the type of subshell:
s = 0, p = 1, d = 2, f = 3
-- For a given shell, the energies of orbitals go:
s < p < d < f

22. shapes and orientations
Quantum numbers (cont.)
3. magnetic quantum number, ml
(ml = integers from –l to l)
-- describes the orientation of an orbital in space
-- You should know the shapes and orientations of
the s, p, and d orbitals:
s, px, py, pz,
dyz, dxz, dxy,
dx2– y2, dz2
shapes and orientations
of d orbitals

23. 4. electron spin quantum number, ms
-- only two values: +½ or –½
(“spin-up” and “spin-down”)
-- Pauli exclusion principle:
No two electrons in an atom
may have the same set of
four quantum numbers
(i.e., an orbital may hold
only two electrons, and
they must have opposite
spins).
Wolfgang Pauli
(1900–1958)

24. (a) Predict the number of subshells in the third shell.
n = 3, so…
l could be 0, 1, or 2
3 subshells
(b) Give the label for each of these subshells.
For: l = 0… 3s
l = 1… 3p
l = 2… 3d
(c) How many orbitals are in each of these subshells?
For: l = 0…
ml = 0
3s: 1 orbital
l = 1…
ml = –1, 0, +1
3p: 3 orbitals
l = 2…
ml = –2, –1, 0, +1, +2
3d: 5 orbitals

25. What are the values of n and l
for the following sublevels?
2s 3d 4p 5s 4f
n = 2
n = 3
n = 4
n = 5
n = 4
l = 0
l = 2
l = 1
l = 0
l = 3
Write the possible sets of the four quantum numbers
for a 4p electron.
4p orbitals
ml : –
4, 1,
–1, +½
4, 1, 0, +½
4, 1,
+1, +½
4, 1,
–1, –½
4, 1, 0, –½
4, 1,
+1, –½

26. ? Write the four quantum numbers of each of the
six 3d electrons of an iron atom.
3d orbitals
ml : –2 –
3, 2,
–2, +½ ?
3, 2,
–1, +½
3, 2, 0, +½
3, 2,
+1, +½
3, 2,
+2, +½
3, 2, ?, –½

27. Brief Review of the Periodic Table
metals: left side of Table; form cations
properties:
ductile
(can pull
into wire)
malleable
(can hammer
into shape)
lustrous
(shiny)
good conductors
(heat and electricity)

28. Brief Review of the Periodic Table (cont.)
nonmetals: right side of Table; form anions
properties:
good insulators
gases or brittle solids
neon
sulfur
iodine
bromine Ne S8 I2
Br2

29. Brief Review of the Periodic Table (cont.)
metalloids (semimetals): “stair” between metals
and nonmetals
(B, Si, Ge, As, Sb, Te, Po, At)
metals
nonmetals
computer chips
Si and Ge
properties:
in-between those of metals
and nonmetals; “semiconductors”
computer chips
Ge and Si 

30. alkaline earth metals:
alkali metals:
group 1 (except H); 1+ charge;
very reactive
alkaline earth metals:
group 2; 2+ charge;
less reactive than alkalis
transition elements:
groups 3–12; variable charges
chalcogens:
group 16; 2– charge; reactive
halogens:
group 17; 1– charge; very reactive
noble gases:
group 18; no charge; unreactive
lanthanides:
elements 58–71
contain f orbitals
actinides:
elements 90–103
main block (representative) elements:
groups 1, 2,
13–18

31. What family of elements has an ns2 valence electron
configuration?
alkaline earth metals

32. Anomalies in the Electron Configurations
Your best guide to writing e– configs is “The Table,”
but there are a few exceptions.
e.g., Cr:
[ Ar ] 4s1 3d5
Cu:
[ Ar ] 4s1 3d10
These exceptions are due
to the closeness in energy
of the upper-level orbitals.
“RuRh…!!”
Other exceptions are…
Mo, Ru, Rh, and Ag.
All of these exceptions have a
single valence-level s electron.