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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) Connect to www.webelements.com 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) Connect to www.webelements.com 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. back 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