Download Fundamental of Atomic Theory, Periodic Law, and the Periodic Table

Fundamental of Atomic
Theory, Periodic Law, and
the Periodic Table
Dr. Pedro M. Pereyra
2006, 2007, 2008, 2010 ©
rev 2011, 2013
Version 1 Revison 2
Expectations
Matter and Chemical Bonding
•
•
define and describe the relationship among atomic
number, mass number, atomic mass, isotope, and radio
isotope;
demonstrate an understanding of the periodic law, and
describe how electron arrangement and forces in atoms
can explain periodic trends such as atomic radius,
ionization energy, electron affinity, and electronegativity
From Empirical to First Theoretical
Concepts
Describing and investigating matter
•
•
•
•
•
A priori thinking in ancient times: first ideas about matter
‚ Kanada
‚ Leucepious
‚ Democritus
From Alchemy to Chemistry
‚ Paracelsus
‚ Boyle
‚ The French
‚ The English
‚ The Germans
‚ The Russians
‚ Dalton’s Atomic - Particle Theory
Classification of matter
Nomenclature of Inorganic Compounds
Types of reactions and kinds of compounds
Classification of Matter
Classification of Matter
From Empirical to Theoretical
Concepts
•
When describing an empirical concept include the
following points:
‚
‚
‚
‚
Precedents leading to the experimental work (hypothesis
and counter or Null hypothesis)
Methods used: indicate variables measured and setup
Results: Qualitative and/or quantitative
Interpretation of results or Laws
From Empirical to Theoretical
Concepts
•
When describing Theoretical concepts include the
following points:
‚
‚
‚
Theoretical hypothesis or empirical results leading to
model
Postulates
New empirical evidence (or empirical evidence used to
support or corroborate the model until it can be considered
a theory)
From Empirical to Theoretical
Concepts
• The
first Periodic Law & the Table of Elements
‚ Mendeleev
‚ Meyer
• Discovery and identification of the Electron:
‚ Faraday, Stoney
‚ Crookes, Roentgen
‚ J.J. Thomson, Millikan
• The quest for the Structure of Matter:
‚ Becquerel, Soddy, Curie, Rutherford
‚ Matter & Anti-matter
‚ Rutherford's Gold Foil Experiment
‚ Moseley’s Periodic Law
Ancient Greek Model
First Atomic Model - Materialist school of thought
•
•
•
Can matter be divided into ever smaller parts? Yes
Is there a limit to how small it can be divided?
‚ Leucipius & Democritus (460-370 BC) porposed that
there is a limit to how small it can be divided
• This limit was a fundamental constituent of matter
• This fundamental forms are indivisible (atomic)
• This fundamental forms must have “eye-hook” to
decide how to combine
‚ Epicurus (341-270 BC) attributes mass to these forms
‚ Asklepiades (~100 BC) considers them capable of
forming clusters.
There was no way at that time to test the validity of this
model
... many, many years later
Dalton 1803
First Empirically supported Atomic Model
•
•
•
What model can one build of matter so it is consistent
with the three basic Laws of chemistry developed from
empirical observations by chemist since the 1700s:
‚ Law of conservation of mass
‚ Law of constant composition
‚ Law of multiple proportions
Dalton postulated:
‚ Matter is made of fundamental particles
‚ These particles are atomic (indivisible) and indestructible
(Atoms)
‚ The atoms making up each element are unique and
identical
• unique mass (size proportional to their mass)
• have fix valences
‚ These particles are the units of chemical change
Dalton’s model was the basic idea behind Mendeleev’s
The Periodic Law
As stated by Mendeleev 1869
•
First statement of the Periodic Law by
Mendeleev
‚
Mendeleev, a Russian Chemist, was one of the first to be
partially successful in arranging the known elements in the
1870's into a chart that would allow the prediction of properties.
He arranged the elements known in those days according to
increasing atomic masses.
‚
The first Periodic Law stated:
• "The properties of the elements are a periodic function of
their atomic masses"
•
Note that there were some inconsistencies in the arrangement of the
elements according to this law
http://www.chemheritage.org/classroom/chemach/peri
odic/meyer-mendeleev.html
Empirical basis of Mendeleev
Periodic Law
•
Chemical properties considered by Mendeleev to
determine periodic behaviour
‚ The relative proportions of Oxygen’s reaction with other
elements (degree of oxidation)
• Li2O - MgO - Al 2O3
‚ The density in the free state or in the form of oxides,
‚ The acidity or basicity of the compounds formed by a
given element, and
‚ The ability of the element to be reduced and to form
double salts
Empirical basis of Mendeleev
Periodic Law
•
Atomic Weights as the organizing factor
‚
“The size of the atomic weight, by the very essence of the
matter, is a number which is not related to the state of division of
the simple body but to the material part which is common to the
simple body and all its compounds. The atomic weight belongs
not to coal or the diamond, but to carbon. The property which
Gerhardt and Cannizzaro determined as the atomic weight of
the elements is based on such a firm and certain assumption
that for most bodies, especially for those simple bodies whose
heat capacity in the free state has been determined, there
remains no doubt of the atomic weight” [Mendeleev, D. THE RELATION BETWEEN
THE PROPERTIES AND ATOMIC WEIGHTS OF THE ELEMENTS
Journal of the Russian Chemical Society, 1: 60-
77 (1869) ].
How masses are determined: see slide 43
Empirical basis of Mendeleev
Periodic Law
•
Interpretation of results
‚
Mendeleev noticed the repetition of chemical properties when
elements were organized in terms of increasing Atomic Weight.
The properties
of the elements
are a periodic
function of their
atomic masses
http://home.clara.net/rod.beavon/periodic1.htm
The consequences of
Electricity and Magnetism to
our understanding of matter
of vacuums, cathodic ray tubes and electrons
First Principles
Örsted’s Principle
•
In 1820, Hans Christian Oersted performed an important
experiment which showed that there was a connection
between electricity and magnetism. When a current was
switched on through a wire, it made a compass needle
turn so that it was at right angles to the wire. The current
had produced a magnetic field strong enough to cause the
compass needle to turn.
•
This fundamental principle is the basis of the galvanometer, the
dynamo, and the motor.
First Principles
Geissler tubes: currents through evacuated gas tubes
The Geissler tube was an evacuated glass cylinder with an electrode at each end. A Geissler tube
contains one or more of the following rarefied (thinned) gasses, such as neon, argon, or air; mercury
or other conductive liquids; or ionizable minerals or metals, such as sodium.
First Principles
Crook’s Tubes: currents through low and high vacuum
tubes
•
First tubes had a only a weak vacuum and showed
regions of fluorescence.
Glowing and non-glowing regions of a Crook’s tube
First Principles
Crook’s Tubes: currents through low and high
vacuum tubes
•
-6
At pressures below 10
to 5×10-8 atmospheres
the rays emanating from
the cathod were
unhindered by gas
molecules and were able
to reach the anode.
First Principles
Röntgen: The discovery of X-rays
•
During 1895 Röntgen was investigating the external effects from the various types
of vacuum tube equipment—apparatus from Heinrich Hertz, Johann Hittorf,
William Crookes, Nikola Tesla and Philipp von Lenard—when an electrical
discharge is passed through them.In early November he was repeating an
experiment with one of Lenard's tubes in which a thin aluminium window had been
added to permit the cathode rays to exit the tube but a cardboard covering was
added to protect the aluminium from damage by the strong electrostatic field that is
necessary to produce the cathode rays. He knew the cardboard covering
prevented light from escaping, yet Röntgen observed that the invisible cathode
rays caused a fluorescent effect on a small cardboard screen painted with barium
platinocyanide (still used for X-ray photography) when it was placed close to the aluminium
window. It occurred to Röntgen that the Hittorf-Crookes tube, which had a much
thicker glass wall than the Lenard tube, might also cause this fluorescent effect.
•
http://en.wikipedia.org/wiki/Wilhelm_R%C3%B6ntgen
The Atom is not atomic
Empirical evidence by J.J. Thomson & Millikan
•
•
•
•
The CRT experiments of Thomson and the oil drop
experiment of Millikan confirm the existence of electrons
as fundamental particles of matter.
J.J. Thomson’s experiment first establishes that all
cathodic rays are due to a single particle with a fix charge
to mass ratio (Re/m)
11
‚ R
=
1.760605
x
10
coulombs/kg
e/m
Millikan’s experiment is the first one to calculate the
charge (qe) of each electron:
‚ q = 1.60217733 x 10 -19 coulombs
e
The mass of the electron (me) could then be calculated
‚ m = 9.136 x 10-31 kg
e
Empirical evidence
Summary of J.J. Thompson’s results
The fact that the electrons form a coherent beam indicates that they all
respond the same way to variations in the magnetic and electric fields.
The strength of the magnetic
field applied to straighten the
beam is proportional to the
mass of the electrons.
The strength of the electric field
applied to shift the beam is
proportional to the charge of
the electrons.
Empirical evidence
Summary of Millikan’s results
The change in falling
speed of negatively
charged standard oil
droplets arranged in
decreasing order
indicated a uniform
change in speed (Äv)
correspinding to the
effect of the charge of
one electron added to
the drops. From this
infromation it was
possible to calculate the
charge of the electron
The Atom is not atomic
J.J. Thomson’s Atomic Model
•
Given the reality of the electron, J.J.
Thomson re-examined Dalton’s model:
‚ Matter is made of fundamental
particles
‚ These particles are divisible into
electrons and a positive mass matrix.
‚ Electrons are embedded into the
positive mass matrix
‚ Some electrons (valence electrons) are
easier to remove or are attracted to the
positive mass giving rise to the
oxidation numbers of the element.
‚ These particles are the units of
chemical change
The Atom is not atomic
Rutherford’s Model of the Atom
(see Gold Foil Experiment)
Matter is mostly empty space
The positive and the negative charge components
of matter exits separate from each other.
Model:
The mass of the atom is concentrated in
a positively charged unit of mass (protons), and
a neutral unit of mass (neutron)
Their numbers determine the final mass of the atom
together they make up a central structure or nucleus
electrons exist somewhere around the nucleus
The Atom is not atomic
The modes of radioactive decay
•
Alpha:
‚
‚
Alpha radiation consists of
positively (+2) charged particles
emitted from the nucleus of an
atom in the process of decay.
These particles are also very
dense which, with their strong
positive charge, precludes them
from penetrating more than an inch
of air or a sheet of paper.
Ther mass was determine to
correspond to the mass of an atom
of Helium .
http://www.libelium.com/es/wireless_sensor_networks_to_control_radiation_levels_geiger_counters/
The Atom is not atomic
The modes of radioactive decay
•
Beta minus:
‚
‚
Beta minus radiation consists of
negatively charged (-1) particles
emitted from an atom in the
process of decay. These particles
are relatively light and can
penetrate somewhat better than an
Alpha particle, though still only
through a few millimetres of
aluminium at best.
These particles turn out to have
the same charge to mass ratio as
electrons
http://www.libelium.com/es/wireless_sensor_networks_to_control_radiation_levels_geiger_counters/
The Atom is not atomic
The modes of radioactive decay
•
Gamma:
‚
Gamma radiation represents one
extreme of the electromagnetic
spectrum, particularly that radiation
with the highest frequency and
shortest wavelength. Gamma rays
can pass through virtually
anything, and are effectively
shielded or absorbed only by
materials of high atomic weight
such as lead.
http://www.libelium.com/es/wireless_sensor_networks_to_control_radiation_levels_geiger_counters/
The Atom is not atomic
The modes of radioactive decay
•
Alpha:
‚
•
Beta:
‚
•
These particles are also very dense which, with their strong positive charge, precludes them from
penetrating more than an inch of air or a sheet of paper. Because of this, Alpha particles are not a serious
health hazard, except when they are emitted from within the body as a result of ingestion, for instance,
when their high energy poses an extreme hazard to sensitive living tissue.
These particles are relatively light and can penetrate somewhat better than an Alpha particle, though still
only through a few millimetres of aluminium at best. If ingested, Beta radiation can be hazardous to living
tissue. A relatively weak form of ionizing radiation detectable on many Geiger counters, generally
dependent on the thickness of the Geiger-Mueller tube wall or the existence of a window at the end of the
tube.
Gamma:
‚
Gamma rays can pass through virtually anything, and are effectively shielded or absorbed only by
materials of high atomic weight such as lead. Gamma rays are produced naturally by the sun and other
bodies in outer space, their transmission to earth being known as "cosmic radiation". A very powerful and
potentially very dangerous type of ionizing radiation detectable on virtually all Geiger counters.
The Atom is not atomic
The modes of radioactive decay
The Gold-foil Experiment
Testing J.J. Thompson’s Atomic Model
The Gold-foil Experiment
Results
The Gold-foil Experiment
Results
The Gold-Foil Experiments
First window to the strucure of the atom
http://www.teachastronomy.com/astropedia/article.aspx?qid=426
Moseley’s Periodic Law
As stated by Moseley
•
Present day Periodic Law by Moseley
‚
‚
It wasn't until 1914 that Moseley, a British Physicist, was able to
determine the atomic numbers of all the known elements using
an experimental technique. Moseley then proceeded to
rearrange the elements according to increasing atomic
numbers and not atomic masses. Moseley's arrangement
seemed to clear up the contradictions and inconsistencies of
Mendeleev's arrangement.
The Periodic Law was restated
• as the generalization that there is a recurring pattern in
the properties of the elements when arranged in order of
increasing atomic number
Empirical basis of Moseley’s
Periodic Law
•
Determination of the Atomic Number
‚
‚
Evidence indicated that the number of protons or atomic number
might increased by steps of one from one element to the next.
Moseley needed some independent function of a nuclear
property that increased in the same pattern, that is, by one for
each element in turn. These would show that the atomic
number was unique for each element. He found it in the K line of
the X-ray spectra of each element
Charles Barkla had demonstrated that the elements emitted
characteristic X-rays, called K and L rays. These X-rays were
independent of the physical or chemical state the element was in
(e.g: atomic, covalent or ionic state). Someone, perhaps Barkla
or Bohr or Moseley, realized that this meant the X-rays were a
characteristic of the nucleus.
Empirical basis of Moseley’s
Periodic Law
•
Determination of the Atomic Number
‚
‚
It turns out that the square root of the frequency of the X-ray emission
moves by a constant value ("one unit") for each one unit move by the atomic
number.
Moseley set about to determine the wavelengths of the K radiation using
recently discovered techniques by the father-and-son team of W.L. Bragg
and W.H. Bragg.
Empirical basis of
Moseley’s Periodic
Law
•
Interpretation of results
‚
Rutherford (in 1914) described Moseley's discovery in this terms:
• "Recently Moseley has supplied very valuable evidence that
this rule [atomic numbers changing by one from element to
element] also holds for a number of the lighter elements. By
examination of the wave-length of the characteristic X rays
emitted by twelve elements varying in atomic weight between
calcium (40) and zinc (65.4), he has shown that the variation of
wavelength can be simply explained by supposing that the
charge on the nucleus increases from element to element by
exactly one unit. This holds true for cobalt and nickel, although
it has long been known that they occupy an anomalous relative
position in the periodic classification of the elements according
to atomic weights."
The Modern Periodic Table
•
The elements are
arranged in vertical
columns known as
Groups. The elements
in each group have
consistently high or
low values for certain
properties. The
horizontal rows of
elements are referred
to as "Periods"
there is a recurring pattern (as described by Mendeleev) in
the properties of the elements when arranged in order of
increasing atomic number (as described by Moseley).
atomic mass units
amu
An atomic mass unit (symbolized AMU or amu) is defined as precisely
1/12 the mass of an atom of carbon-12. The carbon-12 (C-12) atom
has six protons and six neutrons in its nucleus.
One atomic mass unit can be concieved as the average weight of the
mass of a proton and the mass of a neutron.
1 amu = 1.66129 x 10-27kg
The actual mass of a proton (m p) and of a neutron (m n) have been
determined to be:
mp = 1.0073 amu = 1.673 x 10 -27kg
mn = 1.0087 = 1.676 x 10 -27kg
Isotopes
With the understanding that each element is determined by
its number of protons or Atomic Number, it became clear
that the values of the atomic masses determined for each
element were the result of the combination in an element of
“isotopes” - atoms with the same number of protons but
different number of neutrons. The atomic mass of an
element represents the average of its isotopic masses.
For example, the atomic mass of Hydrogen was found to be
1.008amu. If hydrogen would consist of atoms containing
only one proton the atomic mass would have to be equal to
1.000 amu. In reality it is found that Hydrogen consists of a
mixture of three isotopes, hydrogen per se, Deuterium
(conteining one neutron) and the radioactive Tritium
(containing two protons).
Isotopes
•
Table of Isotopic Masses and Natural Abundances
‚
•
http://www.chem.ualberta.ca/~massspec/atomic_mass_abund.pdf
Table of Radioactive Isotope Data
‚
http://www.evs.anl.gov/pub/doc/tbl2-rad-prop.pdf
Isotopes
Isotopes
Isotopes
Isotope mass, abundance & atomic mass
The average atomic mass of an element is the
result of the sum of its isotopes masses times their
relative abundance.
If “M” is the (average) atomic mass of a given
element, and m1, m2, m3, etc. are the masses of
its isotopes and a1, a2, a3, etc, their respective
abundance fractions, the weight average atomic
mass is given by
M = a1m1 + a2m2 + a3m3 + ....
Isotopes
Isotope mass, abundance & atomic mass
For example, Magnesium (Mg) with an atomic
number of 12, is known to be composed of three
isotopes with the following characteristics:
Isotope
24
Mg
25
Mg
26
Mg
isotopic mass
23.9850423amu
24.9858374amu
25.9825937amu
abundance
78.99%
10.00%
11.01%
Confirm that the atomic mass of Magnesium is
24.305amu.
Isotopes
Isotope mass, abindance & atomic mass
•
The abundance of an mixture of isotopes can be
caclulated from the atomic mass and the isotope masses
•
This calculation is easiest for an element with only two
isotopes, for example Lithium.
‚
•
Using the general equation for atomic mass:
• M = a1m1 + a2m2
• And knowing that the atomic mass of lithium is 6.94amu
We can determine the abundances of each isotope in the
mixture.
Isotopes
Isotope mass, abindance & atomic mass
•
Lithium example
‚ M = a1xm1 + a2m2
• M = 6.94
• Isotope masses
•
•
m1= 6.015122 7.59 amu, m2= 7.016004 92.41amu
abundances a1 and a2 = ???
Isotopes
radioactive decay
http://www.es.mq.edu.au/GEMOC/Participants/Research/ADosseto/decay_chains.gif
Isotopes
Thorium decay chain
radioactive decay
http://hepwww.rl.ac.uk/ukdmc/Radioactivity/UTh_chains.html
Isotopes
radioactive decay
The expected
alpha-decay
chain of new
isotope 233Am
and alphaparticle energy
spectrum. In
the spectrum
the decay chain
is observed
with the 6.78
MeV alphaparticle
originating
from 233Am
decay
Overview of Universal Constants
NIST Reference on Constants, Units and Uncertainty
•
Historical introduction to Universal Constants
‚ http://physics.nist.gov/cuu/Constants/introduction.html
‚ http://physics.nist.gov/cuu/Constants/historical1.html
‚ http://physics.nist.gov/cuu/Constants/historical2.html
‚ http://physics.nist.gov/cuu/Constants/historical3.html
‚ http://physics.nist.gov/cuu/Constants/alpha.html
‚ Index of experiments described
• http://physics.nist.gov/cuu/Constants/histindex.html
Max Planck and Albert Einstein
and down the rabbit hole we went ...
Max and Albert in Quantum land
Interconversion of mass &
energy
2
E=mc Einstein’s Equation
The transformation of mass and energy
From the previous information we might have noticed that
the mass of a single proton and a single neutron are both
higher than the average value calculated for 1 amu using
carbon -12.
Were we to calculate from the proton mass and the
neutron mass 1/12 of the weight of a carbon-12 nucleous
one would arrive at the value 1.675 x 10-27kg, which is
larger than the 1.66129 x 10-27kg equivalent for one
atomic mass unit.
The difference in mass ( 0.013 x 10-27kg ) is equivalent to
the amount of matter that is released as energy in the
formation of every proton-neutron pair (nucleon) in the
carbon-12 nucleous
E=mc
2
The transformation of mass and energy
The difference in mass ( 0.013 x 10-27kg ) is equivalent to
the amount of matter that is released as energy in the
formation (fussion) of every proton-neutron pair (nucleon)
in the carbon-12 nucleous.
The amount of energy liberated per nucleon is
1.19x10-12J.
For 12 g of Carbon-12 this value becomes
4.3 x 109J = 4.3 GJ!!!
Enaugh energy to rise the temperature of 1 million liters of
water by one degree!
Blackbody Radiation
Technical Note
Blackbody radiation
A “blackbody” is any object or substance that
absorbs or emits a squwed distribution of the full
electromagentic spectrum of radiation as a function
of its temperature as described by Steffen’s and
Wien’s Laws.
U (J/m2)
Absorptions are a
function of the
volume’s
temperature of
hollow bodies while
emissions are the
function of the
surface’s
temperature of a
body
Blackbody emission spectrum
of a body surface at 2000 K
would have an emission
maximum at 720nm and would
therefore appear a dark
glowng red to the eye.
l (m)
Technical Note
Blackbody radiation
Steffen’s Law: The energy density (U) of
absorption or of emission of a blackbody is
proportional to the fourth power of the body’s
4
temperature (T).
Utotal % T
[Utotal = area under the curve]
U (J/m2)
T1 < T2
l (m)
Technical Note
Blackbody radiation
Wien’s Law: The absorption or emission
maximum (ëMAX) of a blackbody is inverse
propotional to the body’s temperature.
ëMAX % 1/T
U (J/m2)
T1 < T2
l (m)
Technical Note
2
U (J/m )
Blackbody radiation theories
Raleigh-Jean’s Model: The “UV”
catastrophy and the inability of
classical physics to explain
blackbody radiation
l (m)
Technical Note
2
U (J/m )
Blackbody radiation theories
The energy of light is a function of its
frequency (or the inverse of its
wavelength)
The energy is quantized
The intensity of light is a function of
the number of times a given
frequency is emitted.
l (m)
E=hí Planck’s Equation
Energy is quantized
Trying to explain the behaviour of the absorption
or emissions in a Blackbody [ ], Max Planck
discovered that the only way to explain the
observation was to assume energy was emitted
or absorbed in small packets or quanta of
energy called a photon. Light (understood as
electromagnetic energy), although it seemed in
many experiments to travel like a wave (ë@í=c),
its energy interactions with matter were
%
fundamentally those of a particle (photon) .
%waves diffract, while particles carry or transfer momentum.
Light does both.
E=hí
Energy is quantized
The energy of this photon or quantum of
energy, Planck found is determined by the
equation:
E=h<
where < is the frequency of the light.
The equation can be expressed also in terms
of wavelength as:
E = h c/8
E=hí
Energy is quantized
h represents a universal constant, now
known as Planck’s constant.
h = 6.6 x 10-34 Js
These constant is, so to say, the standard of
universal “action” or the “currency” constant
of energy defining all quantized phenomena.
Atomic Emission
Spectroscopy
Basic concepts
Spectrographs,
spectrometers, and
spectrophotometers
• Emission and
Absorption spectra
• Continuous and
discontinuos spectra
•
Atomic Emission
Spectroscopy
Hydrogen Spectrum
visible emisions
UV emissions
Atomic Emission
Spectroscopy
Hydrogen Spectrum
•
•
•
The visible spectrum of light from hydrogen
displays four visible wavelengths at 410 nm,
434 nm, 486 nm, and 656 nm.
The series is know and the Balmer series and
can be calculated by using the Balmer
formula, an empirical equation discovered by
the swiss mathematitian Johann Balmer in
1885.
2
2
1/8 = kBALMER (1/2 - 1/n ); n>2
Atomic Emission
Spectroscopy
Hydrogen Spectrum
•
•
•
Similar series were discovered for the ultra
violet (UV; Lyman series) and infrared (IR, Paschen
series) emissions of the hydrogen atom.
In 1888 the physicist Johannes Rydberg
generalized the Balmer, Lyman, and Paschen
equations for all transitions of hydrogen.
2
2
1/8 = RyH (1/k - 1/n ); k<n
Bohr’s Model
Bohr’s Model of the Hydrogen Atom
• First
postulate:
Electrons exist in orbits
• Second postulate:
The angular momentum of the
hydrogen electron is quantized.
Bohr’s Model
Electrons exists in orbits
Bohr’s Model
angular momentum of the hydrogen electron is quantized
mev rn = n h/2B
where
me is the mass of the electron
v is the speed of the electron
rn is the radius of the nth orbit
n is the orbit number
and n h/2B
is the quantized value allowed for each orbit
Bohr’s Model
Implications of postulates 1 & 2
•
These two postulates lead to the derivation of
two fundamental relationships:
‚
The radii of the orbits that the hydrogen electron can occupy
2
are given by the equation: rn = a0n ; where a0 represents the
radius of the ground state orbit of the hydrogen electron, also
known as Bohr’s radius (a0 . 0.5 D).
‚
The orbital energy levels the hydrogen electron can have, are
2
given by the equation: En = -E0 1/n ; where -E0 represents the
ground energy or ionization energy of the hydrogen electron (E0 = -13.6eV)
Bohr’s Model
Implications of postulates 1 & 2
•
The implication of
the first relationship
is that, the orbital
distances from the
nucleus where one
can find the excited
Hydrogen electron,
are discrete and
increase with the
square of the orbit
number.
Bohr’s Model
Implications of postulates 1 & 2
•
The implication of the
second relationship is that,
the energy an electron can
have, is limited to specific
quantized values. As the
electron is energized, the
difference in energy
between orbits (or levels)
decreases in terms of the
square of the orbit number.
Atomic Theory
postulate connecting theory with evidence
•
3rd postulate part a
‚
When the hydrogen electron is energized (+ÄE),
the electron will jump to a higher “permitted”
orbit.
‚
Upon releasing it’s gained energy (-ÄE) the
electron will “jump” back to lower orbits until it
reaches its ground state.
Atomic Theory
postulate connecting theory with evidence
•
3rd postulate part b:
‚
‚
‚
the energy released will be equivalent to the
difference in the energy between the nth energy
level the electron “jumped from” to kth energy
level it returned to:
2
2
• )E = Eo (1/k - 1/n )
The electron will release its energy in the form of
electromagnetic energy
• ÄE = hí = hc/ë
The corresponding wavelength of the emission is
therefore given by:
• hc/ë = Eo (1/k2 - 1/n2)
• ë = hc / Eo (1/k2 - 1/n2)
Empirical Corroboration of Bohr’s
Model of the Hydrogen Spectrum
Application of Bohr’s Concepts to the calculation of the energy
differences between the proposed electron orbits and their expected
wavelength equivalents
C:\Documents and Settings\Administrator\My Documents\Chemistry\Lab Manual Files\Manual\Spectroscopy\Hydrogen Spectrum & Bohr Model Lab
Eval 2011.wpd
•
•
Theoretical step
‚ Use of a spreadsheet program to
• calculate the matrix (n to k “jumps) of energy differences
in eV (n = {1,2 ..., 7}; k={1,2,...,7}
• convert the matrix of eV values into Joule values
• Calculate the corresponding wavelengths matrix in
nanometres.
Empirical step
‚ Determine the emission spectrum of Hydrogen, Deuterium
and Helium
‚ Determine the error of the readings with respect to their
standard values.
Empirical Corroboration of Bohr’s
Model of the Hydrogen Spectrum
Application of Bohr’s Concepts to the calculation of the energy
differences between the proposed electron orbits and their expected
wavelength equivalents
•
Corroboration
‚ Identify in the calculations those calculated wavelengths
that correspond to the visible range of the spectrum.
‚ Compare the calculated values with the standard values of
the visible range of the Hydrogen or Deuterium spectra
‚ Recalculate the theoretical emissions predicted for
Helium’s two electrons
• Replace Eo = 13.6eV for the corresponding ionization
energies of Helium’s electrons
•
•
•
1st ionization energy = 24.56 eV
2nd ionization energy = 54.42 eV
Compare the visible range calculated values with the
standard visible range values of the Helium spectrum
Empirical Corroboration of Bohr’s
Model of the Hydrogen Spectrum
Application of Bohr’s Concepts to the calculation of the energy
differences between the proposed electron orbits and their expected
wavelength equivalents
•
Corroboration Results
‚ Bohr’s Model of the Hydrogen atom is able to predict the
exact values of the emissions of Hydrogen, we can
therefore conclude that
• The Hydrogen’s electron can exist in orbits around its
nucleus
•
The angular momentum of the electron is quantized
•
When excited, it “jumps” to predictable energy levels and
relaxes back to its ground state by releasing energy in
the form of light with wavelengths corresponding to
discrete “jumps” of predictable energy differences.
Bohr’s Interpretation of the
Hydrogen Spectrum
Paschen series
Balmer series
Lyman series
Empirical Corroboration of Bohr’s
Model of the Hydrogen Spectrum
Application of Bohr’s Concepts to the calculation of the energy
differences between the proposed electron orbits and their expected
wavelength equivalents
•
Limitations of the Bohr Model
‚ Bohr’s Model of the Hydrogen atom is unable to predict the exact
values of the emissions of Helium, we can therefore conclude
that
• The Helium’s electrons motion can not be model by the idea of
planetary orbits around the Helium nucleus.
•
The fact that the emissions are discrete indicates that their
momenta must be quantized.
•
When excited these electrons will “jump” to higher energy levels
and will relax back to their ground state releasing their energy in
the form of light of wavelengths corresponding to discrete
energy differences.
A glimpse of the modern
quantum mechanical model of
atomic structure
Particle-wave nature of
matter and light
The DeBroglie equation
The realization by De Broglie that matter in
motion behaves like waves, particularly at the
atomic level was later proven by the
application of X-ray diffrection crystalography
and the development of the electron
microscope.
2
E = mc ;
E=hc/8;
8 = h/ mv
No more than two electron
per energy level
Pauli’s exclusion principle
Pauli was able to interpret the results of
superfine spectral lines as indicating that
electrons had a “spin” property that
corresponded to two possible magnetic
states (spin up or spin down with corrponding
quantum numbers +½ and - ½)
quantum phenomena can be described or
studied only in terms of their momentum
or in terms of their position but not both
simultaneously
Heisenberg’s exclusion principle
When measuring quantized events the classical view
that a phenomenon would be described by the function
of their forces and their energy resultig in a set of
equations describing their motion and positions was
proving to be elusive in the quantum world of electrons
and atomic particles.
So one can know where something is but not when or
on can know something is in certain sate now but not
where.
Implications to Atomic theory
These facts had a very important impact in further
developmets in atomic theory.
Electrons in motion could not be considered
particles, but more exactly like three dimensional
standing waves. Its description would have to be in
terms only of its quantized momenta (changes of
energy) leaving its position to be descibed by a
probability space.
This lead to Shrödinger’s and Heisenberg’s
Quantum Mechanical Wave model of the atom
From Theory to Facts
• Periodic Trends
Periodic Trends
•
•
Intrinsic Atomic Properties
‚ These are properties that are unique to each atom of a
given element and are independent of the quantity of
material or the interactions among atoms
Bulk Elemental Properties
‚ These are properties that depend on the quantity of matter
or on the interactions among atoms
Periodic Trends
•
•
Intrinsic Atomic Properties
‚ Atomic Size
• Atomic Radius
• Ionic Radius
‚ Ionization Energies
‚ Electron Affinity Energies
‚ Electronegativity
Bulk Elemental Properties
‚ melting point
‚ boiling point
‚ density
Periodic Trends
Intrinsic Trends Explantion
•
All trends are empirically determined to explain them
indicate the following points:
‚ Definition
‚ How the property is measured and units of measurement
‚ What the periodic trend is
‚ Explantion of trend based on the Bohr-Rutherford Atomic
Theory
Intrinsic Atomic Properties
Atomic Size
•
How is Atomic size determined?
‚
‚
‚
•
Atomic size is determined by a variety of scattering methods (X-rays, Neutron bombardment) on crystalline or liquid
samples of the element or its compounds.
The covalent radius is usually interpreted as Atomic radius
Ionic radius depends on the number of electrons gained or lost by the atom
What units are these radii measured in?
‚
‚
Atomic radii are in the 10-10m range - also known as an Angstrom (Å). 1Å = 10-10m.
Many illustrations, however, show these values in the tens to hundreds of pico meters (10-12m)
Intrinsic Atomic Properties
Characteristics of cathionic and anionic radii
The ionic radius of cathions is significantly smaller
than the original radius of the element due to the loss
of valence electrons and the stronger attraction of the
inner electrons
An Anion, on the other hand,
is much larger than its parent
atom due to the fact that the
nuclear charge is unabel to
hold with the same attraction
the increase number of
valence electrons
Intrinsic Atomic Properties
Atomic Size
•
What are the periodic trends of covalent/atomic radii?
‚
‚
Which element has the smallest radius, H or He and why?
Which element has the largest radius and why?
Covalent radius
decreases from
left to right along a
period
• Covalent radius
decreases up each
group.
•
Intrinsic Atomic Properties
explanation of covalent atomic radius periodic trend
•
atomic radius decreases along a period because:
‚ the number of protons increases
‚ causing the Effective Nuclear Charge (Z) to increase
‚ which causes an increase attraction of the electrons
towards the nucleus
‚ resulting in a smaller radius
•
atomic radius decreases up the groups because:
‚ the number of shells decreases
‚ causing the Effective Nuclear Charge (Z) to increase
‚ which causes an increase attraction of the electrons
towards the nucleus
‚ resulting in a smaller radius
Intrinsic Atomic Properties
Ionization Potential or Ionization Energies
•
What is Ionization Energy (IE) or Ionization Potential (IP)?
‚
‚
•
How is IE and IP determined?
‚
•
IE: The ionization energy is a measure of the energy required to remove one
electron from one mole of gaseous atoms or ions. (bulk measurement)
IP: The ionization potential is a measure of the energy required to remove
one electron from an atom or ion. (single event measurement)
Using a mixture of mass spectroscopic methods and electric fields of known
characteristics
• resonance ionization mass spectroscopy (RIMS)
What units is it measured in?
‚
‚
IE: kJ/mol or kJ mol-1 (J: Joules)
IP: eV (electron volts)
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the 20 ionization
energy values
for Calcium.
Notice the trend
of values
corresponds to
the 3 energy
shells present in
calcium
Intrinsic Atomic Properties
Ionization Potential or Ionization Energies
•
What is the periodic trend of Ionization Energies?
‚
Which element has the lowest and which the highest IE values and why?
IE increases from
left to right along a
period
• IE decreases down
each group.
•
Intrinsic Atomic Properties
Ionization Potential or Ionization Energies
•
What is the periodic trend of Ionization Energies?
‚
Which element has the lowest and which the highest IE values and why?
IE increases from
left to right along a
period
• IE decreases down
each group.
•
Intrinsic Atomic Properties
•
Electron Affinity Energies
What is Electron Affinity?
‚
‚
•
•
Electron Affinity is defined as the energy change in an
atom when capturing one electron into its valence shell
If the energy change is negative (releases energy) the
atom is able to retain the captured electron
How is EA determined?
‚ The determination of EA is complex and is arrived at by
calculations from thermoelectric experiments, laser
spectroscopy and other indirect approaches.
What units is it measured in?
‚ EA is measured in kJ/mol and has a negative sign.
(energy released)
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Intrinsic Atomic Properties
Electron Affinity Energies
•
What is the Periodic Trend of Electron Affinities?
EA is “zero” for the
elements of
groups IIA, IIB,
and VIII.
• EA increases most
clearly from left to
right along a
period
• EA decreases in
some groups down
the group. (Partial
trend)
•
Intrinsic Atomic Properties
Electron Affinity Energies
•
What is the Periodic Trend of Electron Affinities?
EA is “zero” for the
elements of
groups IIA, IIB,
and VIII.
• EA increases most
clearly from left to
right along a
period
• EA decreases in
some groups down
the group. (Partial
trend)
•
Intrinsic Atomic Properties
Pauling’s Concept of Electronegativity (÷)
•
How is Electronegativity defined?
‚ "Electronegativity is the power of an atom when in a
molecule to attract electrons to itself." The
electronegativity will depend upon a number of factors
including other atoms in the molecule, the number of
atoms coordinated to it, and the oxidation number for the
atom. There are a number of ways to produce a set of
numbers which represent electronegativity scales. The
Pauling scale is perhaps the most famous.
‚
Intrinsic Atomic Properties
Pauling’s Concept of Electronegativity (÷)
•
What is the Periodic Trend for Electronegativity?
÷ is “zero” for the
top elements of
group VIII.
• ÷ increases from
left to right along a
period
• ÷ decreases in
some groups down
the groups.
• Transition metals
have a more
variable behaviour
•
Intrinsic Atomic Properties
Summary and Explanation
•
In general the intrinsic periodic trends can be explained in
terms of the effects of increase number of protons and
increase number of orbit or electron shells.
An increase of orbits
produces a decrease in
the attractive coulombic
force of the nucleus on
its outer electrons
(effective nuclear
charge Z). As a result
there is an increase in
atomic radius and a
decrease in the
ionization and electron
affinity effects
Intrinsic Atomic Properties
Summary and Explanation
•
In general the intrinsic periodic trends can be explained in
terms of the effects of increase number of protons and
increase number of orbit or electron shells.
An increase of protons
along a period,
produces an increase in
the attractive coulombic
force of the nucleus on
its outer electrons
(effective nuclear
charge Z). As a result
there is a decrease in
atomic radius and an
increase in the
ionization and electron
affinity effects
(Review of empirical process)
Results - Interpretation - Discussion
Periodic Law and Periodic trends are purely empirical
concepts
• The data collected (IE values, EA values, reactivity,
proportionality of elements in compounds, etc.) are examples
of quantitative data.
• The organization of these data in terms of the periodic law
and the periodic table lead to the discovery of patterns
(interpretation)
• The explanation of these patterns in terms of number of
protons and number of orbits (or shells) is an example of the
discussion of results in terms of theories and their connection
to other empirical knowledge (atomic theories, coulombic
forces, etc.)
•
Bulk Elemental Properties
Bulk Elemental Properties
The state variables: Melting and Boiling Point
The melting and
boiling points are
unique to each
substance
• The value of these two
points depend on the
pressure at which the
measurements are
made.
• This dependency is
described by a
Pressure Temperature Phase
Diagram
•
Bulk Elemental Properties
The state variables: Melting and Boiling Point
•
When
comparing
Melting and
Boiling Points is
usually done at
standard
atmospheric
pressure.
Colligative Elemental Properties
State property: Density
•
When comparing densities it must be done for
elements in the same state, usually the solid state
Technical Note
Determination of the molar mass of compounds
•
Atomic, Ionic or molecular masses are now determined
accurately and routinely using a Mass Spectrometer (Mass
Spec or MS).
Technical Note
Determination of the molar mass of compounds
Compounds are subjected to an ionizing beam that brakes the
compounds into smaller ionic components or species
• These ionic species are accelerated and made to pass a
magnet that bends their path
• This strong magnetic field can be modified so that selectively
focuses these ions in relationship to their mass on a detector
•
This technique also
allows to identify complex
compounds, due to the
fact that each compound
has a unique ionization
pattern.
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Technical Note
Blackbody radiation
A “blackbody” is any object or substance that
absorbs or emits a squwed distribution of the full
electromagentic spectrum of radiation as a function
of its temperature as described by Steffen’s and
Wien’s Laws.
Blackbody emission
spectrum of a body
surface at 2000 K
would have an
emission maximum at
720nm and would
therefore appear a dark
glowng red to the eye.
Technical Note
Blackbody radiation
Steffen’s Law: The energy density (U) of
absorption or of emission of a blackbody is
proportional to the fourth power of the body’s
temperature (T).
U% T4
Wien’s Law: The absorption or emission
maximum (ëMAX) of a blackbody is inverse
propotional to the body’s temperature.
ëMAX % 1/T
back
Absorptions are a function of the volume’s temperature of hollow bodies
while emissions are the function of the surface’s temperature of a body