Download General Chemistry: An Integrated Approach

Chapter Seven
Atomic Structure
Views on Atomic Structure
Classical View – electrons
and properties of electrons
Experiments with Light –
Quantum Theory
Quantum View – behavior of
electrons in atoms
EOS
Chapter 7: Atomic Structure
2
Cathode Rays
Cathode rays are the carriers of
electric current from cathode to
anode inside a vacuumed tube
Emit perpendicular
to the cathode
surface when
electricity is passed
through an
evacuated tube ...
... and travel in
straight lines
EOS
Chapter 7: Atomic Structure
3
Cathode Rays
Cause glass and
other materials to
fluoresce
Deflect in a
magnetic field
similarly to
negatively charged
particles
EOS
Chapter 7: Atomic Structure
4
J. J. Thomson’s Experiment
Devised an experiment to find the
ratio of the cathode ray particle’s
mass (me) to the charge (e)
me /e = –5.686 × 10–12 kg C–1
EOS
Chapter 7: Atomic Structure
5
The Electron
Millikan
measured the
charge on an
electron - the
famous “oil
drop”
experiment.
EOS
Chapter 7: Atomic Structure
6
Determined Electron Values
Robert Millikan then determined a value for the
charge
e = –1.602 × 10–19 C
From m/e and the charge, the mass of an electron
was determined to be
m = 9.109 × 10–31 kg/electron
EOS
Chapter 7: Atomic Structure
7
J. J. Thomson – Atomic Model
Thomson proposed an atom with a positively
charged sphere containing equally spaced electrons
inside
Proposed for a hydrogen atom that there was one
electron at the exact center of the sphere
Proposed for a helium atom that two electrons
existed along a straight line through the center, with
each electron being halfway between the center and
the outer surface of the sphere
EOS
Chapter 7: Atomic Structure
8
Raisin Pudding Model
EOS
Chapter 7: Atomic Structure
9
Rutherford’s Model
Ernest Rutherford characterized alpha particles
through an experiment and discovered the positive
charge of an atom is concentrated in the center of an
atom, the nucleus
EOS
Chapter 7: Atomic Structure
10
Rutherford’s Interpretation
EOS
Chapter 7: Atomic Structure
11
Protons and Neutrons
From Rutherford’s experiments, he was able to
determine the amount of positive nuclear charge
The positive charge was carried by particles
called protons
Scientists introduced the atomic number,
which represents the number of protons in the
nucleus of an atom
James Chadwick discovered neutrons in the
nucleus, which have nearly the same mass as
protons and no charge
Chapter 7: Atomic Structure
EOS
12
Mass Spectrometry
A mass spectrometer is a
device that separates positive
gaseous ions according to
their mass-to-charge ratios
A record of the separation of
ions is called a mass
spectrum
EOS
Chapter 7: Atomic Structure
13
Mass Spectrometer
If a stream of positive ions
having equal velocities is
brought into a magnetic
field, the lightest ions are
deflected the most, making
a tighter circle
EOS
Chapter 7: Atomic Structure
14
The Atom – Where Were We?
• The atom has gone through some changes,
where are we now?
• 1. Democritus/Dalton = small, spheres.
• 2. Thomson = plum pudding model.
• 3. Rutherford = planetary model.
• The model is incomplete – it didn’t really
explain where electrons were outside the
nucleus.
New Model of the Atom
• In the early 20th century, a new model of the
atom was proposed.
• This new model evolved as a result of
investigations into the absorption and
emission of light by matter.
• That’s where our story begins now….
Properties of Light
• Light has been known for years to behave
as a wave.
• However, it was discovered that light also
has particle-like characteristics.
Wave Description of Light
• What is light?
• Light is a form of electromagnetic
radiation.
• Electromagnetic radiation = a form of
energy that exhibits wavelike behavior as it
travels through space.
Examples of Electromagnetic
Radiation
• Electromagnetic radiation include X-rays, UV
rays, infrared rays, and visible light.
• What do you think is strong radiation? Weak
radiation?
• Together, all the forms of electromagnetic
radiation form the electromagnetic spectrum.
EM Radiation Spectrum
Visible Light
Parts of a Wave
Parts of a Wave (Definitions)
• c = the speed of a wave which is ALWAYS
3.0 x 108 m/s
 l = wavelength of a wave (usually in units of
nm, m, or cm)
• This l referred to as lambda.
• The wavelength is the distance between
corresponding points on adjacent waves.
Parts of a Wave
Parts of a Wave (Definitions)
 n = refers to the frequency of a wave
 n is known as “nu”.
• The frequency of a wave is defined as the # of
waves that pass a given point in a specific
time.
• Frequency has units of “waves/s”, “1/s”, “s-1”,
or “Hz = Hertz”.
Parts of a Wave (Definitions)
• Amplitude (a) = is the height or brightness
(loudness) of a wave.
• The amplitude of a wave is measured in
units of m, nm, or cm.
Calculations
• The overall formula we will use is this:
• c = ln
HINTS
• HINT #1: Use a triangle. c is up top.
• HINT #2: 1 nm = 1 x 10-9 m
• HINT #3: frequency has MANY units.
Remember that!
• HINT #4: c is ALWAYS 3.0 x 108 m/s
• HINT # 5: wavelength needs to be in “m”.
Examples
• I have a wave that has a wavelength of 1.20
x 10-9 m. What is the frequency of this
wave?
• I have a wave that has a frequency of 5.2 x
1016 Hz. What is the wavelength of this
wave?
Examples (Cont.)
• I have a wave that has a wavelength of 750
nm. What is the frequency?
• What part of the EM spectrum is this wave
located?
• I have a wave with a frequency of 3.5 x 1017
s-1. What is the wavelength?
• What part of the EM spectrum is this wave
located?
POP Quiz!!!!
• Given: Wavelength of 500 nm; Find =
frequency of the wave.
• What part of the EM is this wave?
• Given: Frequency of 1.88 x 1015 Hz; Find
= wavelength of the wave in BOTH m and
nm.
• What part of the EM is this wave?
The Photoelectric Effect
• Photoelectric effect uses the frequencies of
various radiation.
• Photoelectric effect = the emission of
electrons from a metal when light shines
on the metal.
• What frequency of light do YOU think
would eject or emit electrons from a metal?
The Photoelectric Effect
• Certain types of light, such as RED and
ORANGE, do NOT hit metals and get
electrons ejected.
• However, BLUE, INDIGO, and VIOLET will.
• Examples include the solar calculator, papertowel dryers, electronic doors.
Light – Wave AND Particle?
• The photoelectric effect helped to explain
that particles of light (or photons) were
what ejected these electrons.
• This suggested the light not only had wavelike properties, but also particle-like
properties.
Particle Properties of Light
• German physicist Max Planck suggested
that objects emit energy in small packets of
photons, referred to as quanta.
• A quantum of energy is the minimum
quantity of energy that can be lost or
gained by an atom.
• E = hn
E = hn
• E = energy, in Joules, of a quantum of
radiation.
n = frequency of radiation, in Hz.
• h = Planck’s constant =
6.6261 x 10-34 J s.
• This equation allows us to calculate the
energy of EM radiation.
Examples
• Infrared light has a frequency of 7.29 x 1014
Hz. What is the energy associated with this
light?
• The energy of a photon of light is found to
be 4.55 x 10-19 J. What is the frequency of
this photon?
Toughie!
• A wave of violet light has a wavelength of
about 400 nm.
• What is (a) the frequency of this light?
• And (b) the energy associated with this
light, in Joules?
Another tough one…
• Calculate the wavelength emitted in the far
UV that corresponds to an energy of 1609
kJ/mol photons.
Chapter 7: Atomic Structure
39
The Hydrogen-Atom Line Emission
Spectrum
• Elements, such as hydrogen, produce various
“lines” or emissions of light when current is
passed through them.
• Ground state = the lowest energy state if an
atom.
• The ground state is where atoms would like to
be.
Emission Spectra
• Excited state(s) = state(s) in which an atom has a
higher potential energy than the ground state.
• When electrons get “zapped” by photons of energy,
they go from the ground state to an excited state.
• When an electron gets “tired” in the excited state, it
emits energy, usually some color of visible light.
Emission Spectra
• When elements emit light into specific
frequencies of visible light, it is referred to as a
line-emission spectrum.
• Continuous spectrum = the emission of a
continuous range of frequencies of EM
radiation.
• Elements don’t follow a continuous spectrum –
they emit specific frequencies of light.
Bohr Model of the H-Atom
• Niels Bohr, a Danish physicist, proposed a
hydrogen-atom model that linked the
electron to the photon.
• He suggested the 1 electron in an H-atom is
in an “energy level” closest to the nucleus.
• He stated electrons move in “orbits” of
energy, and the lowest energy level is
referred to as ground-state energy level.
Bohr Model of the H Atom
• Bohr stated that the electron absorbed a
fixed amount of energy (a photon) to go
from the ground state to a higher energy
state.
• The electron absorbed or emitted a fixed
amount of energy as it moved from various
energy levels.
Bohr Model of the H Atom
• Ephoton = E2-E1
• This Bohr model of the atom seemed to
work – but ONLY for the H atom.
• WHY?!?!?!?
• H only has 1 electron…….
Wave Motion
Caused by a displacement in
a medium
Characterized by height of
crest (or depth of trough)
EOS
Chapter 7: Atomic Structure
46
The Wave Nature of Light
Electromagnetic waves originate from the
movement of electric charges
The movement produces fluctuations in electric and
magnetic fields
Chapter 7: Atomic Structure
47
Characterizing Waves
Electromagnetic radiation is characterized by its
wavelength, frequency, and amplitude
Wavelength (l) is the distance between any
two identical points in consecutive cycles
EOS
Chapter 7: Atomic Structure
48
Characterizing Waves
Frequency of a wave is the number of cycles of
the wave that pass through a point in a unit of time
Amplitude of a wave is its height: the distance
from a line of no disturbance through the center of
the wave peak
EOS
Chapter 7: Atomic Structure
49
The Electromagnetic Spectrum
The electromagnetic spectrum is largely invisible to the
eye
EOS
Chapter 7: Atomic Structure
50
The Electromagnetic Spectrum
• We can feel some radiation through other senses
(infrared)
• Sunburned skin is a sign of too much ultraviolet
radiation
• Materials vary in their ability to absorb or transmit
different wavelengths
– Our bodies absorb visible light, but transmit
most X rays
– Window glass transmits visible light, but
absorbs ultraviolet radiation
EOS
Chapter 7: Atomic Structure
51
Continuous Spectra
White light
passed
through a
prism
produces a
spectrum –
colors in
continuous
form.
EOS
Chapter 7: Atomic Structure
52
The Continuous Spectrum
l ~ 650 nm
l ~ 575 nm
l ~ 500 nm
l ~ 480 nm
l ~ 450 nm
The different
colors of
light
correspond to
different
wavelengths
and
frequencies
EOS
Chapter 7: Atomic Structure
53
Line Spectra
Light passed
through a
prism from an
element
produces a
discontinuous
spectrum of
specific colors
EOS
Chapter 7: Atomic Structure
54
Line Spectra
The pattern of lines emitted by excited atoms of an
element is unique
= atomic emission spectrum
EOS
Chapter 7: Atomic Structure
55
Quantum Theory –
Black Body Radiation
Planck proposed that the vibrating atoms in a heated
solid could absorb or emit electromagnetic energy
only in discrete amounts
The smallest amount of energy, a quantum, is
given by:
E = hv
where h is Planck’s constant: = 6.626 × 10–34 J s
Planck’s quantum hypothesis states that energy can be
absorbed or emitted only as a quantum or as whole
multiples of a quantum
EOS
Chapter 7: Atomic Structure
56
Quantum View of
Atomic Structure
Bohr’s Hydrogen Atom
• Niels Bohr followed Planck’s and Einstein’s lead by
proposing that electron energy (En) was quantized.
• The electron in an atom could have only certain allowed
values of energy (just as energy itself is quantized).
• Each specified energy value is called an energy level of the
atom:
En = –B/n2
– n is an integer, and B is a constant (2.179 × 10–18 J)
– The negative sign represents force of attraction.
• The energy is zero when the electron is located infinitely
far from the nucleus.
Example 7.5
Calculate the energy of an electron in the second
energy level of a hydrogen atom.
The Bohr Model of Hydrogen
When excited, the
electron is in a higher
energy level.
Excitation: The atom
absorbs energy that is
exactly equal to the
difference between two
energy levels.
Each circle represents an
allowed energy level for the
electron. The electron may be
thought of as orbiting at a fixed
distance from the nucleus.
Emission: The atom
gives off energy—as
a photon.
Upon emission, the
electron drops to a
lower energy level.
Line Spectra Arise Because …
Transition from
n = 3 to n = 2.
Transition from
n = 4 to n = 2.
• … each electronic
energy level in an
atom is quantized.
• Since the levels are
quantized, changes
between levels must
also be quantized.
• A specific change
thus represents one
specific energy, one
specific frequency,
and therefore one
specific wavelength.
Bohr’s Equation …
• … allows us to find the energy change (Elevel) that
accompanies the transition of an electron from one energy
level to another.
Initial energy level:
Final energy level:
–B
–B
Ei = ——
ni2
Ef = ——
nf2
• To find the energy difference, just subtract:
–B
–B
1
1
Elevel = —— – —— = B — – —
nf2
ni2
ni2
nf2
• Together, all the photons having this energy (Elevel)
produce one spectral line.
Example 7.6
Calculate the energy change, in joules, that occurs
when an electron falls from the ni = 5 to the nf = 3
energy level in a hydrogen atom.
Example 7.7
Calculate the frequency of the radiation released by the
transition of an electron in a hydrogen atom from the n
= 5 level to the n = 3 level, the transition we looked at in
Example 7.6.
Pop Quiz!
• Calculate the wavelength, in nanometers,
that corresponds to the radiation released by
the electron energy-level change from ni = 6
to nf = 1 in a hydrogen atom.
• B = 2.179 x 10-18J
• Elevel =
Energy Levels and Spectral Lines for Hydrogen
What is the (transition that produces
the) longest-wavelength line in the
Balmer series? In the Lyman series?
In the Paschen series?
Ground States and Excited States
• When an atom has its electrons in their lowest possible
energy levels, the atom is in its ground state.
• When an electron has been promoted to a higher level, the
electron (and the atom) is in an excited state.
• Electrons are promoted to higher levels through an electric
discharge, heat, or some other source of energy.
• An atom in an excited state eventually emits a photon (or
several) as the electron drops back down to the ground
state.
Example 7.8
A Conceptual Example
Without doing detailed calculations,
determine which of the four electron
transitions shown in Figure 7.19
produces the shortest-wavelength
line in the hydrogen emission
spectrum.
De Broglie’s Equation
• Louis de Broglie’s hypothesis stated that an object in
motion behaves as both particles and waves, just as light
does.
• A particle with mass m moving at a speed v will have a
wave nature consistent with a wavelength given by the
equation:
l = h/mv
• This wave nature is of importance only at the
microscopic level (tiny, tiny m).
• De Broglie’s prediction of matter waves led to the
development of the electron microscope.
Example 7.9
Calculate the wavelength, in meters and nanometers,
of an electron moving at a speed of 2.74 × 106 m/s.
The mass of an electron is 9.11 × 10–31 kg, and 1 J = 1
kg m2 s–2.
Uh oh …
• de Broglie just messed up the Bohr model of the
atom.
• Bad: An electron can’t orbit at a “fixed distance”
if the electron is a wave.
– An ocean wave doesn’t have an exact location—neither
can an electron wave.
• Worse: We can’t even talk about “where the
electron is” if the electron is a wave.
• Worst: The wavelength of a moving electron is
roughly the size of an atom! How do we describe
an electron that’s too big to be “in” the atom??
Electrons – Waves and particles
• Remember where we are:
• Electrons can behave as BOTH waves and
particles.
• Louis de Broglie suggested that electrons
could gain specific amounts of energy
(quanta) based on specific frequencies of
light.
De broglie
• de Broglie also suggested that electrons have other
“wave-like” properties.
• #1. Electrons can be bent, or diffracted, like light
waves.
• #2. Electrons bumping into each other can cause
interference, when beams of electrons overlap.
• Interference can cause either a reduction in energy or an
increase in energy.
Heisenberg’s Uncertainty principle
• In 1927, German physicist Werner Heisenberg
helped answer the following question:
• If electrons are both particles and waves, then
where are they in the atom?
• Heisenberg Uncertainty Principle: it is
impossible to determine, simultaneously, both the
position and the velocity of any particle, including
an electron.
Schrodinger Wave Functions
• Erwin Schrodinger, an Austrian physicist,
used this information, along with some
“hard-core” calculus, to help describe 4
characteristics of the electron.
• He called this – Quantum theory.
Electron Characteristics
• Before we discuss the 4 characteristics, we need to
discuss the probability of finding an electron.
• Where would you bet an electron would most
definitely be found? Least found?
• Orbital – a 3-D region around the nucleus that
indicates the probable location of an electron.
4 Characteristics
• The 4 characteristics of an electron are known as
the 4 quantum numbers.
• Characteristic #1: The principle quantum #.
• The principle quantum number (n) indicates
the main energy level occupied by an electron.
• Can only be a positive integer (n = 1, 2, 3, 4, …)
4 Characteristics (cont.)
• Characteristic #2: The angular momentum
quantum #.
• The angular momentum quantum # (l) indicates
the shape of the orbital. l = 0, 1, 2, ….,(n-1)
•
•
•
•
Shape #1:
Shape #2:
Shape #3:
Shape #4:
s – spherical
p – dumbbell or figure-8
d – cloverleaf
f
4 Characteristics (cont.)
• Characteristic #3: The magnetic quantum #.
• The magnetic quantum # (m) indicates the
orientation (+ or -) of an orbital around the
nucleus.
m=0, +/-1, +/-2,….+/-l
• Characteristic #4: The spin quantum #.
• The spin quantum # indicates whether an electron
in an orbital spins clockwise or counterclockwise.
# of ELECTRONS per energy level
• We can determine the # of electrons per
energy level using the following formula:
• 2n2 (where n is the energy level)
• When n = 1, there are 2 electrons.
• When n = 2, there are 8 electrons.