Atomic Structure and the Periodic Table

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16 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Atomic Structure and the
Periodic Table

The electronic structure of an atom
determines its characteristics

Studying atoms by analyzing light
emissions/
absorbtions


Spectroscopy: analysis of light
emitted or absorbed from a
sample


Instrument used =
spectrometer


Light passes through a slit to
become a narrow beam


Beam is separated into
different colors using a prism
(or other device)


Individual colors are recorded
as spectral lines

Electromagnetic radiation


Light energy


A wave of
electric

and
magnetic

fields


Speed = 3.0 x 10
8

m/s


Wavelength (

)
=
distance
between adjacent peaks


Unit =
any length unit


Frequency (

)

=
number of
cycles per second


Unit =
hertz (Hz)

Relationship between properties of
EM waves


Wavelength x frequency = speed of light




v

= c


Calculate the frequency of light that has a wavelength of 6.0 x 10
7

m.

Calculate the wavelength of light that has a frequency of 3.7 x 10
14

s
-
1

Visible Light


Wavelengths from 700
nm (
red
) to 400 nm
(
violet
)


No other wavelengths are
visible to humans

Quanta and Photons


Quanta: discrete
amounts


Energy is quantized


restricted to discrete
values


Only quantum mechanics
can explain electron
behavior


Analogy: Water flow

Another analogy for quanta


A person walking
up steps


his
potential energy
increases in a
quantized
manner

Photons


Packets of
electromagnetic energy


Travel in
waves


Brighter light = more
photons

passing a point
per second


Higher
energy

photons
have a higher frequency
of radiation


Planck

constant

h

= 6.63 x 10
-
34

J

s



E =
h
v

The energy of a photon is directly

p
roportional to its frequency

In a laboratory, the energy of a photon of blue
light with a frequency of 6.4 x 10
14

Hz was
measured to have an energy of 4.2 x 10
19

J.


Use Planck’s constant to show this:

E = (6.63 x 10
-
34

J∙s) x (
6.4 x
10
14

1/s) =
4.2 x 10
19

J

Deriving Planck’s constant

Evidence for photons


Photoelectric effect


the
ejection of
electrons

from
a
metal

when exposed to
EM radiation


Each substance has its
own “threshold”
frequency

of light needed
to eject electrons


Determining the energy of a photon


Use Planck’s constant!


What is the energy of a
photon of radiation with
a frequency of 5.2 x 10
14

waves per second?

E =
h
v

Another problem involving photon
energy


What is the energy of a
photon of radiation
with a wavelength of
486 nm?

Louis de Broglie


proposed that matter and
radiation have properties of both waves and
particles (Nobel Prize 1929)


Calculate the wavelength
of a hydrogen atom
moving at 7.00 x 10
2

cm/sec


=
h



m



m

= mass



= velocity

h

=
Planck’s constant

Hydrogen spectral lines

Balmer

series:


n
1

= 2 and
n
2

= 3,
4
, …




Lyman series (UV lines):


n
1

=
1
and
n
2

= 2, 3, …


Atomic Spectra and Energy Levels


Observe the hydrogen
gas tube, use the prism to
see the frequencies of EM
radiation emitted


Johann
Balmer



noticed
that the lines in the visible
region of hydrogen’s
spectrum fit this
expression:

v
= (3.29 x 10
15

Hz) x
1

-

1

4


n
2

n

= 3, 4, …

Rydberg equation: works for all lines
in hydrogen’s spectrum

v
= R
H

x
1

-

1

n
1
2

n
2
2

R
H

= 3.29 x 10
15

s
-
1


Rydberg Constant

Energy associated with electrons in
each principal energy level


Energy of an
electron in a
hydrogen atom

-
2.178 x 10
-
18

joule

n
2

E =

n

= principal quantum number

Differences in Energy Levels of the
hydrogen atom

Use the Rydberg Equation

OR

Use the expression for each

energy level’s energy in the following equation:


E =
E
final



E
initial


Assumed e
-

move in circular orbits
about the nucleus


Only certain orbits of definite
energies are permitted


An electron in a specific orbit has a
specific energy that keeps it from
spiraling into the nucleus


Energy is emitted or absorbed ONLY
as the electron changes from one
energy level to another


this energy
is emitted or absorbed as a photon


Niels

Bohr’s contribution


When an e
-

makes a transition from one energy level
to another, the difference in energy is carried away by
a
photon


Different excited hydrogen atoms undergo different
energy transitions and contribute to different spectral
lines

Summary of spectral lines

The Uncertainty Principle


Werner
Heisenberg


The dual nature of matter
limits how precisely we
can simultaneously
measure location and
momentum of small
particles


It is IMPOSSIBLE to know
both the location and
momentum at the same
time

Atomic Orbitals


more than just
principal energy levels


Erwin Schrodinger
(Austrian)


Calculated the shape of
the wave associated with
any particle


Schrodinger equation


found mathematical
expressions for the shapes
of the waves, called
wavefunctions

(psi)


Born’s

contribution


Max Born (German)


The probability of
finding the electron
in space is
proportional to


2

Called the “probability
density” or “electron density”

Atomic Orbital


the
wavefunction

for an electron in an atom


s



high probability of e
-

being near or at nucleus


ELECTRON IS NEVER AT
THE NUCLEUS IN THE
FOLLOWING ORBITALS:


p



2 lobes separated by a
nodal plane


d



clover

shaped


f



flower

shaped


More about orbitals


Each orbital can
hold
2

electrons


Orbitals in the
same subshell
have equal
energies

Quantum numbers


like an
“address” for an electron

n = principal quantum
number

As n increases

*

orbitals become
larger


e
lectron is


farther from
nucleus

more often


h
igher in
energy


l
ess tightly bound to nucleus




l

= angular momentum quantum
number


Values:
0 to
n



1


Defines the shape of the orbital

Quantum numbers

Value of
l

0

1

2

3

Letter
used

s

p

d

f


m
l

=

the magnetic quantum number


Orientation of orbital in space


(i.e.
p
x

p
y

or
p
z
)


Values: between


l

and
l
, including 0



Quantum numbers

Example: for
d

orbitals, m can be
-
2,
-
1, 0, 1, or 2

For p orbitals, m can be
-
1, 0, or 1


m
s

= the spin number


When looking at line spectra, scientists
noticed that each line was really a
closely
-
spaced pair of lines!


Why? Each electron has a SPIN


it
behaves as if it were a tiny sphere
spinning upon its own axis


Spin
c
an be + ½ or
-
1/2


Each represents the direction of the
magnetic field the electron creates

Quantum numbers


n = 4, l = 1, m
l

=
-
1,
m
s

= +1/2



Describe the electron that has the
following quantum numbers:

Principal level 4

4p orbital

p
x

orbital

s
pin up

Are these sets of quantum numbers
valid?


3, 2, 0,
-
1/2



2, 2, 0, 1/2

YES!

Level 3

3d orbital

3d
xz

Spin down

NO!

Level 2

2
d orbital


does

n
ot exist!

Electron configuration: rules

1.
Aufbau

principle


electrons fill
lowest

energy
levels first

2.
Pauli exclusion principle


only 2 electrons may
occupy each
orbital, must
have opposite spins

3.
Hund’s

rule


the lowest
energy is attained when
the number of electrons
with the same spin is
maximized


(because electrons
repel


each other)

Energy level specifics


s and d orbitals are close
in energy


Example


4s

electrons have slightly
lower energy than
3d

electrons


The
s

electrons can
penetrate to get closer to
the nucleus, giving them
slightly lower energy

4s

3d

Noble Gas Configuration


A shorter electron
configuration


Write the symbol for the
noble gas BEFORE the
element in brackets


Write the remainder of
the configuration


Examples:


Cl





Cs


Special rules


One

electron can move
from an
s orbital
to the
d
orbital

that is closest in
energy


Only happens to create
half or whole
-
filled d
orbitals


Examples: Cr, Cu