Transcript Atomic Structure, etc.

Atomic Structure and
Periodicity
Electromagnetic Radiation
The Nature of Matter
The Atomic Spectrum of Hydrogen
The Bohr Model
The Quantum Mechanical Model
Quantum Numbers
Electromagnetic Spectrum
10-12
4x10-7
10-10
10-8
5x10-7
10-4
10-2
6x10-7
1
102
104
7x10-7
Electromagnetic Radiation

Gamma

X rays

Ultraviolet

Visible (400-700nm)

Infrared

Microwaves

Radio waves

Power waves
Electromagnetic Radiation

Three primary characteristics
 Wavelength (…lambda)
 Frequency (…nu)
 Speed (c)
Wavelength

Distance between two consecutive crests or troughs
of a wave

Measured in m or nm, typically
Frequency

Number of wave cycles per second that pass a
given point in space

Cycle is understood in SI language

Measured in 1/s or s-1, also known as a hertz (Hz)
Speed

Constant, known as the speed of light

2.9979 x 108m/s

Since the speed of a wave is constant, then frequency
and wavelength must vary inversely

c = 
Problem #1

A wave is known to have a frequency of 5.09 x
1014Hz. What is its wavelength and what type of
electromagnetic radiation is it?
Electromagnetic Spectrum
10-12
4x10-7
10-10
10-8
5x10-7
10-4
10-2
6x10-7
1
102
104
7x10-7
Problem #1
5.89 x 10-7 m
Visible
Yellow-orange
The Nature of Matter

Matter and energy (in the form of light) were
thought to be distinct until 1900
 Matter was made of particles that had mass,
took up space, and could absorb or emit any
quantity of energy
 Light was made of waves that were massless and
of unknown location (delocalized)
Max Planck (1858-1947)

German physicist

Observed that heated solid
bodies emitted energy only in
specific whole-number multiples

They were multiples of the
quantity “h”

h is known as Planck’s constant
and has a value of 6.626 x 1034J•s
Max Planck (1858-1947)

Thus, the change in internal
energy of a system is
represented by

E = h

“h” came to be known as a
quantum

Proved that energy is indeed
quantized not continuous
Problem #2

Cuprous ions will emit 4.41 x 10-19J when heated
to approximately 1200C. What is the wavelength
of the light emitted and what color is it?
Electromagnetic Spectrum
10-12
4x10-7
10-10
10-8
5x10-7
10-4
10-2
6x10-7
1
102
104
7x10-7
Problem #2
4.50 x 10-7 m
blue-green
Albert Einstein

Proposed the electromagnetic
radiation may be viewed as a
stream of particles, known as
“photons”

Said that the energy of a
photon equaled the change in
internal energy that a system
experienced

Ephoton= h = hc/
Albert Einstein

In 1905, he proposed that energy
has mass and put forth the famed
equation

E = mc2 or m = E/c2

Thus,
m = E = hc/ = h
c2
c2
c

Established the phrase “dual
nature of light”
Prince Louis-Victor Pierre Raymond
de Broglie

Proved that the opposite of the
dual nature of light was true

Showed that particles also
exhibited wave properties

de Broglie’s equation replaces the
speed of light with the speed of
the particle
m= h
v
or
= h
mv
Problem #3

Compare the wavelength of an electron with a
mass of 9.11 x 10-31 kg traveling at a speed of
1.00 x 107 m/s with that of a tennis ball with a
mass of 0.0089kg traveling at 42.5 m/s.
Electron—7.27 x 10-11 m
Tennis ball—1.75 x10-33 m
Diffraction

Scattering of light from a regular array of points or
lines..make a diffraction pattern

Proves the wave properties of particulate matter

Pattern results from constructive interference
 Light spots

And destructive interference
 Dark spots
Matter

Exhibits particulate and wave properties

Big bits have tiny wavelengths and have more
particulate properties

Itty-bitty bits have larger wavelengths and behave
more like waves than particles

Medium bits have fairly equal representation of
particles and waves
Atomic Spectrum of
Hydrogen

When H atoms are excited, they emit the excess
energy according to the electromagnetic spectrum

This is known as an emission spectrum

It is not continuous as white light through a prism
is

Rather, it is known as a line spectrum

Verifies quantization of energy emission
Line Spectrum of
Hydrogen
The Bohr Model

developed in 1913 by Danish
physicist, Niels Bohr

Proposed that the electron in H
moves in particular circular orbits

Agreed with the emission spectrum
of hydrogen assuming the angular
momentum of the electron
occurred in specific increments
The Bohr Model

provides the equation that gives the
energy levels available in hydrogen

E = -2.178 x 10-18 J(Z2/n2)
 n represents the integer indicating
the distance from the nucleus
(will eventually be shown to be
the energy level)
 Z represents the nuclear charge
which is +1 for hydrogen
The Bohr Model

If a hydrogen electron is excited to
a higher energy level and then falls
back down to the 1st energy level
(the ground state), then the
associated energy change can be
determined.

E = Ef – Ei
E = -2.178 x 10-18 J(1/nf2 – 1/ni2)
Problem #4

Determine the wavelength of light emitted when a
hydrogen electron falls from the 6th energy level to
the 1st energy level. What type of electromagnetic
radiation is this?
9.38 x 10-8 m
ultraviolet
The Quantum Mechanical Model

Begun by de Broglie

Remember the dual nature of
light and the idea that all matter
traveled in waves and as particles?
The Quantum Mechanical Model

Erwin Schrödinger (1887-1961)

Austrian physicist

Treated electron pathways as
standing waves

Designated wave functions
(functions of x, y, and z coordinates)
that we peons tend to call orbitals

Proved orbitals are not circular
The Quantum Mechanical Model

Werner Heisenberg (1901-1976)

German physicist

“We cannot always assign to an
electron a position in space at a
given time, nor follow it in its
orbit, so that we cannot assume
that the planetary orbits
postulated by Niels Bohr actually
exist. Mechanical quantities,
The Quantum Mechanical Model

such as position, velocity, etc.
should be represented, not by
ordinary numbers, but by abstract
mathematical structures called
matrices.“

Proposed the above postulate at
the age of 23!!

Later came up with his famed
Uncertainty Theory
Heisenberg’s Uncertainty Principle

There is a fundamental limitation
to just how precisely we can know
both the position and momentum
of a particle at a given time.

x • (mv) > h/4



x is the uncertainty in position
(mv) is the uncertainty in
momentum
h is Planck’s constant
Probability




Shown is that of the hydrogen 1s orbital
Distribution graph shows a
darker image where an electron tends to
be found more
frequently
Approximately 90% of the time,
the electron may be found in this sphere
Also called an electron density map
Electron Configurations

Energy level

Sublevel
s
p
d
f

# electrons
Electron Configurations
Electron Configurations
Electron Configurations
Orbital Diagrams
3px
3py
3pz
2py
2pz
3s
E
2px
2s
1s
Orbital Diagrams
3px
3py
3pz
2py
2pz
3s
E
2px
2s
1s
Orbital Diagrams
3px
3py
3pz
2py
2pz
3s
E
2px
2s
1s