# Atomic Structure and the Periodic Table

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16 Νοε 2013 (πριν από 4 χρόνια και 7 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

Light energy

A wave of
electric

and
magnetic

fields

Speed = 3.0 x 10
8

m/s

Wavelength (

)
=
distance

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

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

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
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
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

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

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

Each orbital can
hold
2

electrons

Orbitals in the
same subshell
have equal
energies

Quantum numbers

like an

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