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Unformatted text preview: CHM CHM 25 – Spring 2009 Chapter 7 Light & Matter Li atte
Prof. R.S. Miller Mill ATOMIC ATOMIC STRUCTURE AND PERIODICITY WHY ARE CHEMICAL PROPERTIES PERIODIC? ARE CHEMICAL PROPERTIES PERIODIC?
Isaac Isaac Newton and classical mechanics ... good for classical baseballs and planets, not so good for atoms What What we already know ... atoms = protons and neutrons in the nucleus; electrons = outside the nucleus the nucleus electrons outside the nucleus The The issue now: let's be a bit more detailed about what/where the electrons are. Why? THAT'S WHERE THE CHEMISTRY IS! THE CHEMISTRY IS! Quantum Quantum mechanics ... incorporation of wave and ... particle aspects of matter into a single comprehensive th theory The The early 20th Century was the century of the electron. James James Clerk Maxwell (1865) ... ... light is electromagnetic radiation waves ... wavelength (λ) and wave (λ) frequency frequency (ν) hertz ... amplitude ... nodes IMPORTANT EQN: λν λν = c
where where c = 3.00 x 108 m / s Note that the radiation with th th the the shortest wavelength has the highest frequency (i.e., inversely related). Classification of electromagnetic radiation Classification of electromagnetic radiation. Behavior of Waves Behavior of Waves
Waves refract or bend when they pass from Waves one medium to another with different densities. Diffraction Diffraction is the bending of electromagnetic radiation as it passes around the edge of an object object or through narrow openings. Interference is the interaction of waves that Interference is the interaction of waves that results results in either reinforcing their amplitudes or canceling them out. Refraction Refraction Diffraction and Interference Diffraction and Interference Atomic Spectrum of Sodium Atomic Spectrum of Sodium Absorption Spectra Absorption Spectra Types of Spectra Types of Spectra
Atomic emission spectra consist of Atomic emission spectra consist of bright bright lines on a dark background. Atomic absorption spectra consist of characteristic series of dark lines produced produced when free gaseous atoms are illuminated by external sources of radiation. radiation. History History of electronic structure:
Planck – (18581947) – studied blackbody (1858radiation (heated bodies emit light). Classical theory predicts continuous increase of intensity with wavelength. Planck’s revolutionary proposal that ENERGY, LIKE MATTER, IS DISCONTINUOUS. energy can only be absorbed or released from atoms in certain amounts called quanta. The relationship between energy and frequency is E = hν where h is Planck’s constant (6.626 × 1034 Planck constant (6 J·s). This shattered idea that energy of matter was continuous said it was was continuous, said it was quantized (packets quantum). quantized (packets = quantum). Established idea that energy has particle properties. particle properties The The retina of a human eye can detect light when radiant energy incident on it is at least 4.0 x 1017 J. For light of 660 nm wavelength how many photons does this 660.0 nm wavelength, how many photons does this correspond correspond to?
E = hc/λ (note: equation is written per photon – energy is usually hc/ per kJ/mol kJ/mol when dealing w/ reactions) E = hc/λ = (6.626 x 1034 J s)(3.00 x 108 m/s)/(6.60 x 107 m) hc/ E = 3.01 x 1019 J/photon 4.0 4.0 x 1017 J x 1 photon 3.01 x 1019 J = 1.3 x 102 photons The Photoelectric Effect and Photons
Einstein (1879Einstein – (18791955) – studied photoelectric photoelectric effect. Proposed EM is quantized. Photons – Photons stream of light particles stream of light particles. If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal point at which electrons are ejected from the metal. The electrons will only be ejected once the threshold frequency reached threshold frequency is reached. Below the threshold frequency, no electrons are ejected. Above the threshold frequency, the number of electrons ejected depend on the intensity of the light. Photoelectric effect Photoelectric effect Line Line spectrum of hydrogen
Balmer: discovered that the lines in the visible line spectrum of hydrogen fit simple equation. line spectrum of hydrogen fit a simple equation. Later Rydberg generalized Balmer’s equation to:
1 ⎛ RH =⎜ λ ⎝h ⎛ ⎞⎜ 1 − 1 ⎞ ⎟ ⎟⎜ 2 2 ⎠⎝ n1 n2 ⎟ ⎠ where RH is the Rydberg constant (1.096776 × 107 m1), is the Rydberg constant (1 h is Planck’s constant (6.626 × 1034 J·s), n1 and n2 are integers (n2 > n1). Bohr’s model Bohr model
Bohr (1885Bohr (18851962) – developed quantum mechanical model for H atom. Electron can only occupy certain El “orbits” or “energy levels”. E = 2.178 x 1018 (1/n2)  Joule units lowest energy state = ground state other energy states = excited states • Colors (line spectra) from excited gases arise because electrons move between energy states in the atom. Model fails to describe any other atom except H, but it is a great start! El Electronic transitions in th the Bohr model for for the hydrogen atom. Bohr model Bohr model The first orbit in the Bohr model has n = 1, is closest to the nucleus and has negative closest to the nucleus, and has negative energy by convention. The furthest orbit in the Bohr model has n close furthest orbit in the Bohr model has to infinity and corresponds to zero energy. Electrons in the Bohr model can only move in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hν). The amount of energy absorbed or emitted on movement between states is given by ΔE = E f − Ei = hν Bohr Model Bohr Model
We can show that
⎛1 hc 1⎞ ΔE = hν = = − 2.18 × 10−18 J ⎜ 2 − 2 ⎟ ⎜n λ ni ⎟ ⎝f ⎠ ( ) When ni > nf, energy is emitted. When nf > ni, energy is absorbed. Problems with the Bohr Model Problems with the Bohr Model
The The Bohr model applies only to one electron atoms electron atoms. The The Bohr model doesn’t account for the observed spectra of multielectron observed spectra of multielectron elements elements or ions. The movement of electrons in atoms is The movement of electrons in atoms is much much less clearly defined than Bohr allowed. The Wave Behavior of Matter The Wave Behavior of Matter
de de Broglie (18921987) – duality principle – both matter and (1892energy have both particle and wave properties. Knowing that light has a particle characteristics, it seems reasonable to ask if matter has wave characteristics. Using Einstein’s and Planck’s equations, de Broglie showed: h λ= mv
The momentum, mv, is a particle property, whereas λ is a wave property. de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small noticeable effects if the objects are small. de Broglie wavelength and velocity de Broglie wavelength and velocity 1.) What is the de Broglie wavelength (in m) What is the de Broglie wavelength (in m) of of a baseball weighing 145 g and traveling at 156 km/h? at 156 km/h? 2.) what velocity would an electron w/ mass 9.11 x 1031 kg need for its de Broglie wavelength to be that of red light (750 wave th li (750 nm)? nm)? Electrons Electrons as Waves
De De Broglie reasoned that an electron in that an electron in a hydrogen hydrogen atom could behave as a circular wave oscillating around wave ill the the nucleus. If If electrons are moving around the nucleus in a continuous manor the continuous manor, the state state of the electron must be described by a quantum number quantum number, n. The Uncertainty Principle
Heisenberg’s Uncertainty Principle: on the
mass scale of atomic particles, we cannot determine exactly exactly the position, direction of motion, and speed position direction of motion and speed simultaneously. For electrons: we cannot determine their momentum and position simultaneously. If Δx is the uncertainty in position and Δmv is the uncertainty in momentum, then uncertainty in momentum, then h Δx·Δmv ≥ 4π Quantum Quantum Mechanics
Schrödinger proposed an equation that contains both wave and particle terms contains both wave and particle terms. Solving the equation leads to wave functions (Ψ (Ψ). The wave function gives the shape of the electronic orbital. The square of the wave function Ψ2, gives the probability of finding the electron (i.e., the electron density (3D) for the atom) electron density (3D) for the atom). To To describe orbitals, we need quantum numbers: n, numbers: n, l, ml Quantum Quantum numbers
1.) Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the becomes larger and the electron is further from the nucleus. 2.) Azimuthal Quantum Number, l. This quantum number depends on the value of number depends on the value of n. The values of l The values of begin at 0 and increase to (n  1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and forbitals. th 3.) Magnetic Quantum Number, ml. This quantum number depends on l. The magnetic quantum number has integral values between  l and + l. Magnetic quantum numbers give the 3D orientation of each orbital. Electron spin? Electron spin?
Line spectra of many electron atoms show each line as a closely spaced pair of lines. Stern and Gerlach designed an experiment to determine why. A beam of atoms was passed through a slit and into magnetic field and the atoms were then into a magnetic field and the atoms were then detected. Two spots were found: one with the electrons spots spinning in one direction and one with the electrons spinning in the opposite direction. 4th quantum number number
Since electron spin is quantized, we define ms electron spin is quantized we define = spin quantum number = ± ½. Pauli’s Exclusions Principle: no two Exclusions Principle two electrons can have the same set of 4 quantum numbers Therefore two electrons in the same numbers. Therefore, two electrons in the same orbital must have opposite spins. sorbital sOrbitals
•All sorbitals are spherical. •As n increases, the sorbitals get larger. •As n increases, the number of nodes increase. •A node is a region in space where the probability of finding an electron is zero. At a node, Ψ2 = 0 •For an sorbital, the number of nodes is (n  1). sorbitals (a) (a) The probability distribution for the the hydrogen 1s orbital in three dimensional space dimensional space. (b) The probability of finding the electron at points along a line drawn from the nucleus outward outward in any direction for the hydrogen hydrogen 1s orbital. porbitals
There are three porbitals px, py, and pz. The three porbitals lie along the x, y and li z axes of a Cartesian system. The letters correspond to allowed values of ml of 1, 0, and +1. The orbitals are dumbbell shaped. As n increases, the porbitals get larger. the get larger All porbitals have a node at the nucleus. porbitals p orbitals orbitals dorbitals & forbitals
There are five d and seven forbitals. are five seven Three of the dorbitals lie in a plane bisecting the bisecting the x, y and zaxes. Two of the dorbitals lie in a plane aligned along the x, y and zaxes. th Four of the dorbitals have four lobes each. One dorbital has two lobes and a collar. Representation of Representation of forbitals Orbital Orbital energy levels for the hydrogen hydrogen atom. The The orders of the energies of the orbitals in the the first three levels of polyelectronic atoms. Electron configurations Electron configurations
Electron configurations tells us in which orbitals configurations tells us in which orbitals the electrons for an element are located. Three rules:
electrons fill orbitals starting with lowest n and moving upwards; no two electrons can fill one orbital with the same spin (Pauli); for degenerate orbitals, electrons fill each orbital degenerate orbitals electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule). Electron Configurations of Ions Electron Configurations of Ions
Start with the configuration for the Start with the configuration for the neutral neutral atom, then add or remove electrons from the valence shells to electrons from the valence shells to make make the desired ion. Atoms or ions that are isoelectronic with each other have identical numbers and configurations configurations of electrons. An An ion having a +4 charge and a mass of 52.00 g/mol has 2 electrons with principal quantum number n = 1, 8 electrons with n = 2, and 10 electrons with n = 3. Supply answers to the following questions: electrons with Supply answers to the following questions: the the atomic number for the ion _______________ the the total number of s electrons _______________ the the total number of p electrons _______________ the the total number of d electrons _______________ the the electron configuration of the neutral atom _______________ atom Mendeleev's Mendeleev's early periodic table, published in 1872. Note the spaces left for missing elements with atomic masses 44, 68, 72, 100. — = 44
— = 68 — = 72
—= 100 Atomic properties & periodic trends: Atomic atomic radii
Consider a simple diatomic Consider molecule. The The distance between the two nuclei is called the bond distance. If If the two atoms which make up the molecule are the same, then half the bond distance is called the covalent radius of the atom. Atomic radii Atomic radii
•Atomic size varies consistently through the periodic table.
↓ As we move down a group, the atoms become larger. → As we move across a period, atoms become smaller. •There are two factors at work: principal quantum number, n, and the effective nuclear charge, Zeff. Sizes of Atoms Sizes of Atoms Screening and Penetration Screening and Penetration
Zeff = Z – S Zeff2 En =  RH 2 n Orbital Orbital Penetration and Effective Effective Nuclear Charge
Orbital penetration occurs when an Orbital penetration occurs when an electron electron in an outer orbital has some probability of being close to the nucleus probability of being close to the nucleus
Penetration Penetration ability follows this order: s>p>d>f Effective Effective nuclear charge (Zeff) is the (Z attractive force toward the nucleus tt th experienced by an electron in an atom. Trends in the Sizes of Ions Trends in the Sizes of Ions
Ion Ion size is the distance between ions in an ionic compound. compound. Ion Ion size also depends on nuclear charge, number of electrons, and orbitals that contain the valence electrons. electrons, and orbitals that contain the valence electrons. Cations Cations vacate the most spatially extended orbital and are smaller than the parent ion. small th th Anions add Anions add electrons to the most spatially extended lar orbital and are larger than the parent ion. Cationic Radii Cationic Radii Anionic Radii Anionic Radii Radii of Atoms and Ions Radii of Atoms and Ions Isoelectronic species Isoelectronic species
All the members of an isoelectronic All the members of an isoelectronic series series have the same number of electrons electrons. As nuclear charge increases in an isoelectronic series the ions become smaller: ll O2 > F > Na+ > Mg2+ > Al3+ Periodic trends: Ionization energy Periodic trends: Ionization energy
The The first ionization energy, I1, is the amount of energy required to remove an electron from a gaseous atom: Na (g) → Na+ (g) + eeThe The second ionization energy, I2, is the energy required to remove an electron from a gaseous ion: Na Na+ (g) → Na 2+ (g) + eNa The The bigger the ionization energy, the more difficult it is to remove the electron remove the electron. Trend: Ionization Trend: ↓ Ionization energy decreases down a group and → increases across a period. increases across period Ionization Energy Trends Ionization Energy Trends Successive Ionization Energies (kJ/mol) Successive Ionization Energies (kJ/mol)
Elements H He Li Be B C N O IE1 1312 2372 5249 520 897 897 801 7296 12040 1758 15050 21070 2426 3660 4617 4581 5298 24682 32508 6201 7465 7465 37926 46956 9391 52976 IE2 IE 3 IE4 IE5 IE6 1087 2348 1402 2860 1314 3383 10956 13304 ...
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This note was uploaded on 02/22/2011 for the course CHEM 25 taught by Professor X during the Spring '06 term at Lehigh University .
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