Table of Contents Chapter 7 - Atomic Structure

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Page 7
-
1

Table of Contents

Chapter 7
-

Atomic Structure


I.

ELECTROMAGNETIC RADI
ATION:

................................
................................
.............

2

T
HE
E
LECTROMAGNETIC
S
PECTRUM

................................
................................
..............................

2

II.

HOW DOES THIS AFFECT

OUR STUDY OF CHEMIST
RY?

................................
....

4

III.

EARLY QUANTUM THEORY

................................
................................
..........................

4

M
AX
P
LANCK
(1858
-
194
7),

A
G
ERMAN
P
HYSICIST
,

................................
................................
.......

4

L
IGHT AS
P
ARTICLES


P
HOTOELECTRIC
E
FFECT
.

................................
................................
...........

5

W
AVE
P
ROPERTIES OF
M
ATTER
:

L
OUIS DE
B
ROGLIE
(1892
-
1987)

................................
.................

6

H
YDROGEN
L
INE
S
PECTRA
&

T
HE
B
OHR
M
ODEL OF THE
A
TOM

................................
....................

7

Johann Balmer (1825
-
1898) and Johannes Rydberg (1854
-
1919)

................................
............

7

Niels Bohr (1885
-
1962) A Danish Scientist

................................
................................
...............

7

IV.

THE WAVE MODEL OF TH
E ATOM

................................
................................
.............

9

H
EISENBERG
U
NC
ERTAINTY
P
RINCIPLE

................................
................................
..........................

9

Warner Heisenberg (1901
-
1976)

................................
................................
...............................

9

Max Born (1882
-
1970)

................................
................................
................................
...............

9

S
CHRÖDINGER
W
AVE
E
QUATION
(1926)

................................
................................
........................

9

Erwin Schrödinger (1887
-
1961), an Austrian Scientist

................................
.............................

9

V.

QUANTUM NUMBERS

................................
................................
................................
....

10

Orbitals
................................
................................
................................
................................
.....

11

Orbital Shapes (based on 2nd QN, l)

................................
................................
.......................

11

Shells and Subshells

................................
................................
................................
.................

12

Practice with Quantum Numbers

................................
................................
.............................

12




Page 7
-
2

Chapter 7
-

Atomic Structure

There are periodic trends that can be explained by atomic structure, for which we
need to understand a litt
le physics.

I.

Electromagnetic Radiation:

-

Energy transport in the form of _______

-

James Maxwell described radiation in terms of oscillating elec
t
ro
-
magnetic fields

-

EMR
encompasses radio waves, microwaves, IR radiation, visible light, UV
radiation, X
-
ray
s,

-
rays; visible tight is a form of _______________

The Electromagnetic Spectrum


In EMR visible light of different v or


correspond to different colors.

Wave motion characterized by
frequency

or
wavelength
, and the wave velocity.

____________
,

, is t
he number of waves or cycles per second that pass a given
point in space


Units:
s
-
1
or cycles per sec or Hz

____________
,

, is the distance from crest to crest in a wave


Units: nm (10
-
9
m) or Å (angstroms = 10
-
8
cm or 10
-
10
m)


Page 7
-
3

v and


are inversely propor
tional to each other

(as one goes up the other goes down)



ν
λ
c




Since all EMR travels at the same speed,

-

If you have a short


(like a short step) you
need to take steps more frequently to keep up (have

a higher frequency).

-

Conversely, if you have a long wavelength, you need to have a smaller
frequency (take fewer steps).


For EMR,
-

velocity in
--
vacuum

is


c = 2.9979 x 10
8

m/s, ____________________

Intensity

is proportional to the _____________.

Ener
gy

is inversely proportional to the _____________.

Short wavelengths have
high

energy.

Long wavelengths have
low

energy.

There are
two types of waves
:

-

______________ waves

like waves in the ocean


any number of cycles are possible

-

______________ waves

lik
e a guitar string


only whole numbers of cycles are possible.

(This is the type that is applicable to our studies of the atom.)

All forms of Electromagnetic Radiation:

-

Travel at the __________________ (2.9979 x 10
8

m/s)

-

Have an ______________ component

-

Ha
ve a ____________ component

-

Have a dual __________ and ________ nature


Lecture Problem #
1.

What is the frequency of light which has a


of 100. nm?



Page 7
-
4

II.

How Does This Affect Our Study of Chemistry?

Some properties of matter could not be explained by

Rutherford’s model of the atom:

(Dense positively charged nucleus with e
-

freely occupying the non
-
dense
exterior.)

1.

The presence of ______________
rather than a complete spectrum
when elements were heated.








2.

The “Ultraviolet Catastrophe”


When m
atter is heated, (stove coils for
example) they give of different colors at
different temperatures


(called:
black body radiation
)


The intensity of the radiation did not
continue to increase as the frequency
increased the way that classical physics
of

the time predicted.


III.

Early Quantum Theory


Max Planck (1858
-
1947), a German Physicist,

Attempted to explain these phenomena.


In 1900 he theorized that black body radiant energy was __________, and could only
have _________________.


He then made the ass
umption that atoms/molecules absorb or emit energy in small
packages or ___________.



Page 7
-
5

Plank’s Equation

for the energy of
_____________
:



h
E


Since
therefore
λ
c
ν
ν
λ
c




λ
hc
E



Where



= _____________ of the radi
ation


h =
6.626x10
-
34
J∙sec

(Planck’s Constant)


Lecture Problem #
2.

How many photons are in 4.00 x 10
-
17

J of energy produced from orange light
with a wavelength of 600. nm?











Light as Particles


Photoelectric Effect.


Discovered by Alb
ert Einstein in 1905.

-

If you shine light on a metal, it
will give off an _____________.

-

It has to be light of sufficient

____________.

(You cannot substitute a lot of
(high intensity) low energy/long
wavelength particles for a fewer
high energy/short wave
length
particles.


(Just like you can’t substitute a bunch of ping
-
pong balls for a bowling ball!!!)


Einstein explained the photoelectric effect by extending Planck’s idea of quantized
black body radiation to all _______.


Page 7
-
6

Examples of:


Quantized

Not Quan
tized


_____________

_____________


_____________

_____________


Wave Properties of Matter: Louis de Broglie (1892
-
1987)


-

In 1925 de Broglie thought: if light, which is a wave, can have a particle
nature, then why can’t __________ (especially electrons) ha
ve a

___________________?

-

He used Einstein’s and Planck’s equations to derive a relationship between the
mass (in kg) of a particle and its wavelength (in m) at a certain velocity (in
m/s).


in
fromEinste
Planck
from
2
mc
E
λ
hc
E






_
__________
mc
h
mc
hc
λ
mc
λ
hc
2
2
for
true
only
is
this






If we substitu
te c with the velocity of the particle:


mv
h
λ
:
Equation
s
Broglie'
De


Good for the


of moving ________.


Lecture Problem #
3.

What is the De Broglie wavelength (in nm) of a hydrogen molecule (m=3.35x10
-
27
kg)
moving at a velocity of 1.84x10
3
m/s ?


We k
now that a
2
2
s
m
kg
J



and h is in units of J∙sec







Page 7
-
7

Hydrogen Line Spectra & The Bohr Model of the Atom


Johann Balmer (1825
-
1898) and Johannes Rydberg (1854
-
1919)

-

examined the four visible lines in the spectrum of the
hydrog
en

atom.

-

played around with these numbers and eventually figured out that all four
wavelengths fit into the
Rydberg Equation
:



Where
R
=1.097x10
7
/m (
Rydberg Constant
)


and n=3, 4, 5…(for a 1 e
-

system)



From this they concluded that for:


n=3

red

(656.3 nm)


n=4

blue
-
green

(486.1 nm)


n=5

blue

(434.0 nm)


n=6

indigo

???


Lecture Problem #
4.

Calculate the wavelength of light emitted (in nm) when an electron falls from the n=6
to the n=2 level in the hydrogen atom.










Niels Bohr (1885
-
1962) A Danish Scientist

-

In 1913 he proposed a new model of the atom that attempted to better explain
atomic line spectra and disproved J.J. Thompson’s “Plum Pudding” model.

-

Electrons move in circular ____________ around the nucleus.

-

The closer the orbit t
o the nucleus, the lower its ______________.

-

Each orbit has a specific energy that has a _______________ value (n).

-

The lowest energy orbit is called the _____________________.

-

Electrons can move from one orbit to another.

Going to a higher energy orbit __
____________ energy.

Returning to a lover energy orbit ___________ energy.


Emitted energy is usually in the form of _________.









2
2
n
1
2
1
R
λ
1

Page 7
-
8


The lines studied by Rydberg and
Balmer all ended in n=___ for a
reason.


For n
f
=2 the

E for the transition put
the em
itted EMR in the _________
portion of the spectra. These were
called the ____________ series.


For n
f
=1 the

E for the transition put
the emitted EMR in the _________

portion of the spectra (large

E
means small

). These were called
the _____________seri
es.


For n
f
=3 the

E for the transition put
the emitted EMR in the _________

portion of the spectra (small

E
means long

). These were called
the _____________series.


Beyond the Paschen series is the Bracket series (n
f
=4) and Pfund series (n
f
=5).


Bohr
calculated the energy of
any given level

as:
2
n
Rhc
E



Rhc=1312 kJ/mol


The energy difference between any two levels is given by:














2
i
2
f
n
1
n
1
Rhc
ΔE

If you know the ____________________ involved.



λ
hc
ΔE



If you k
now the _______________ of the emission.


Unfortunately, Bohr’s model only successfully explained the spectrum of the H atom.


Efforts were made to modify his theory (e.g., elliptical orbits) but were unsuccessful.


We had to move to a whole new theory.


Page 7
-
9

IV.

T
he Wave Model of the Atom


Heisenberg Uncertainty Principle

Warner Heisenberg (1901
-
1976)

In studying the works of Bohr and DeBroglie concerning the wave nature of the
electron stated that:


Because matter has a particle and wave properties, it is impossib
le to determine
the
exact

_____________ and the
exact

______________ (or energy, velocity)
of a particle ___________________.


To see something, we must shine light on it, but small particles change position and
energy when struck by photons of light.


Heisenberg related the uncertainty in the position (

x) to the uncertainty in the
momentum (

p) as follows:







3.14159
π
constant;
s
Planck'
h
where
4
π
h
Δp
Δx







and


m
ΔΔ
v
m
Δ
Δp





Max Born (1882
-
1970)

Interpreted Heisenberg’s Uncertainty Principle as:


If we choose to k
now the __________of an electron in an atom with only a small
uncertainty, we must accept a relatively large uncertainty in its ___________ in
the space around an atom’s ____________.


This means that we can only develop areas of high ________________ of f
inding an
electron of a given energy in a certain ____________ of space.


Schrödinger Wave Equation (1926)

Erwin Schr
ö
dinger (1887
-
1961), an Austrian Scientist

Developed a mathematical wave function (

H
)(psi) to describe the ____________
for finding a give
n electron for the hydrogen atom in certain regions of space.


The equation is long and complex, but includes _________ important variables:


Page 7
-
10

V.

Quantum Numbers

The three variables that come out of the wave equation are: n, l, m
l


n

These

-

are quantum variab
les


-

have a restricted set of allowed values


-
known as

quantum numbers .

l

m
l


Different solutions were attempted for the wave equation and allowed values were
found to be:

QN

Dependence

Possible Values

n

independent

1, 2, 3, etc. in integers

l

dependent on ___

0 to (n
-
1) in integers

m
l

dependent on ___

-

l

to +

l

in integers


There are “sets” of possible quantum numbers


Lecture Problem #
5.

Try writing the possible sets of n, l, and m
l

that can be obtained when n=3.



n

l

m
l




















The solutions to the wave equation (

2
) were plotted to see what the affect of the
different variables was on the probability distribution.


Symbol

Name

Affect

n

primary QN

The ______of the probability region (the energy level)

l

angular mome
ntum


QN

The __________of the probability region

m
l

magnetic QN

The _____________in space of the probability region


Page 7
-
11

Orbitals

The density of the probability points varies with
the distance from the nucleus.

-

The density is not homogeneous.

-

The probability r
egion extends to infinity (but
probability gets very small).

-

We enclose the 90% probability area in a surface
known as _____________.


Orbital Shapes (based on 2nd QN, l)



When
l

=0

the orbital is
_________________

Known as an ___ orbital.

-

There are __
_ nodal planes.

-

There is ___ lobe


When
l

=1
, the orbital looks like a _____________

Known as a ___ orbital.

-

There is ___ nodal plane.

-

There are ___ lobes






When
l

=2
, the orbital looks like a double dumbbell or a dumbbell with a doughnut.

Known as a
___ orbital.

-

There are ___ nodal plane.

-

There are ___ lobes
(or 2 lobes and a
doughnut)


When
l

=3

(
see bottom
right for shape
)

Known as a ___ orbital.

-

There is ___ nodal
plane.

-

There are ___ lobes


(after f comes g, h, i, etc)


Page 7
-
12

Shells and Subshells

A
s
hell

is a grouping of orbitals with the same values ____ .


A
subshell

is a grouping of orbitals with the same values of ________.

e.g. 3p (a set of 3 orbitals) or 4d (a set of 5 orbitals)


Within each shell there are ____ subshells.

e.g. when

n=1 there i
s 1 subshell (1s)


n=2 there are 2 subshells (2s, 2p)


n=3 there are 3 subshells (3s, 3p, 3d)


n=4 there are 4 subshells (_______________)



Practice with Quantum Numbers


When n=4 what are the possible values of l?


When l=2, what are the possible values
of m
l
?


For a 4s orbital, what are the possible values of n, l, m
l
?





For a 3f orbital, what are the possible values of n, l, m
l
?





What is wrong with each set of QNs?

n=2, l=2, m
l
=0


n=3, l=0, m
l
=
-
2


n=0, l=0, m
l
=
-
1