Electromagnetic Radiation

Chapter 6: The Periodic Table and Atomic Structure Electromagnetic Radiation Atomic Spectra The Bohr Atom Quantum Mechanical Model of the Atom Wave Mechanics Quantum Numbers and Electron Orbitals Interpreting and Representing Orbitals of the Hydrogen Atom Electron Spin Multi-electron Atoms Electron Configurations Periodic Trends in Atomic Properties Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium. A wave transmits energy. The Electromagnetic Radiation Visible light is a small portion of the electromagnetic radiation spectrum detected by our eyes. Electromagnetic radiation includes radio waves, microwaves and X-rays. Described as a wave traveling through space. There are two perpendicular components to electromagnetic radiation, an electric field and magnetic field. Wavelength,, is the distance between two corresponding points on a wave. Amplitude is the size or height of a wave. Frequency,,is the number of cycles of the wave passing a given point per second, usually expressed in Hz. The Wave Nature of Light The Wave Nature of Light The fourth variable of light is velocity. All light has the same speed in a vacuum. c =.9979458 x 10 8 m/s The Wave Nature of Light Refraction is the bending of light when it passes from one medium to another of different density. Speed of light changes. Light bends at an angle depending on its wavelength. Light separates into its component colors. The product of the frequency and wavelength is the speed of light. c = Frequency is inversely proportional to wavelength. 1

The Wave Nature of Light Electromagnetic radiation can be categorized in terms of wavelength or frequency. Visible light is a small portion of the entire electromagnetic spectrum. Constructive and Destructive Interference Quantum Theory Blackbody Radiation: Max Planck, 1900: Energy, like matter, is discontinuous. Energy consists in discrete packets (quanta) E = h = quantum of energy h = 6.63x10-34 J s ( Planck s constant) The Evidence for Light as Particles: Einstein based the idea of light as particles based on his analysis of the photoelectric effect: electrons are ejected from the surface of a metal when light strikes it. Photoelectric effect Observations 1. No electrons are ejected when light is below a threshold frequency, ν 0, regardless of the intensity of the light. Threshold frequency depends on the metal. For light above the threshold frequency, the kinetic energy of the ejected electrons increases linearly with the frequency of light. KE e ( - o ) Note KE is independent of the light s intensity 3. For light above the threshold frequency, the number of ejected electrons increases with the intensity of the light The Photoelectric Effect Photoelectric Experiments a) For > 0, the number of electrons emitted is independent of frequency. Value of 0 depends on metal used. b) As light intensity increases, the number of photoelectrons increases. c) As frequency increases, kinetic energy of emitted electrons increases linearly for > 0. d) The kinetic energy of emitted electrons is independent of light intensity.

Explanation of the Photoelectric Effect 1. A minimum energy is required to remove each electron from a metal surface (E 0 ). This energy is called the work function of the metal.. Light is a stream of particles (photons) striking the surface, each with energy E = hν. Increasing the intensity of light increases the number of photons, but not their energy. 3. If a photon has an energy greater than E 0, it will eject an electron. The left-over energy of the photon is converted to the kinetic energy of the freed electron: KE e = ½mv e = hν - E 0. 4. If each photon has enough energy to eject an electron, then the greater the number of photons (i.e. the greater the intensity of light), the more electrons are ejected. Electromagnetic Radiation Exhibits Wave Properties and Particulate Properties So, light is a wave AND a stream of particles. i.e. it shows the behaviour of both. This is known as the dual nature of light: 5. If each photon does not have enough energy to eject an electron, then no electrons will be ejected, regardless of how many photons strike the surface (i.e. regardless of the intensity of light). Electromagnetic Radiation Example Microwave ovens operate at.45 GHz. 1. What is the wavelength of these microwaves?. What is the energy a single photon? Quantum Theory and Atomic Structure First, these new ideas explained something which could not have been previously understood: the emission spectrum of the hydrogen atom. For comparison, consider sunlight refracted by a prism: white light contains all the visible wavelengths (it has a continuous spectrum) 3. What is the energy of a mole of photons? 4. How many photons per second are being produced in a 900 W microwave oven H Atom Spectrum When a high-voltage spark is passed through H, some excited H atoms are generated which emit light. When this light is refracted by a prism, it is found to contain discrete lines of specific wavelengths: the hydrogen emission spectrum is a line spectrum. H Atom Spectrum Light emission is due to a loss of energy by hydrogen electrons. Each emitted photon is a packet of energy which was lost by an electron. Since photons of only certain wavelengths are emitted, this indicates that only discrete quanta of energy can be lost (or gained) by an electron within the hydrogen atom (consistent with Planck s view of energy). If hydrogen electrons lose or gain energy in quanta, then only certain energies are possible for the hydrogen electron (quantized energy levels). 3

H Atom Spectrum A photon is emitted as an excited electron drops from a higher to a lower energy level. The energy of the emitted photon (hν) is therefore equal to the difference between the final and initial energy levels of the electron. hc Change in Energy Empirically it was found that the wavelengths of observed lines in the H atom spectrum could fit to the equation 1 1 1 R H n1 n where n 1,, 3, ; n n 1, n, n 3, 1 and R 109,677.58 cm or.178 x10 H 1 E h Frequency of emitted light 1 1 Wavelength of emitted light 1 18 J The Bohr Atom Bohr proposed that the electron in the hydrogen atom moved around the nucleus in various allowed circular orbits at specified distances from the nucleus. Allowed orbits were described by integer numbers (n = 1,, 3, ) which Bohr determined by assuming that the angular momentum of the electron was quantized. h mevr n n n v m r In the model, the numbers increase as the electron gets further from the nucleus. e The Bohr Atom Bohr model - electrons orbit the nucleus in stable orbits. Although not a completely accurate model, it can be used to explain absorption and emission. Electrons move from low energy to higher energy orbits by absorbing energy. Electrons move from high energy to lower energy orbits by emitting energy. Lower energy orbits are closer to the nucleus due to electrostatics. Electronic Transitions in the Bohr Model for the Hydrogen Atom Quantitative Features of the Bohr Atom Equating attractive force of the coulombic potential between the electron (charge e) and nucleus (charge Ze) and the centrifugal force of the rotating electron. n m e Ze m v mer e 4 r r r o solving for r 4o n r m Ze e n a Z 4 o where a0 5.9 pm is the Bohr radius m e e 0 Quantitative Features of the Bohr Atom The kinetic energy of the electron is 1 1 n n n KE mev me m r m r e e n me a0 Z The potential energy of the electron is Ze PE 4 r e m PE 4 0 e 0 Ze e Z n 4 a n 40 a0 Z 0 0 Z 1 Z mea0n a 0 m a n e 0 Z m a Z me a e o n 0 n 4

Quantitative Features of the Bohr Atom The total energy of the electron is KE + PE Z Z Z E KE PE m a n m a n m a n 1 Z E n E H e o e o where EH m a e o e o 18 4.36x10 From his model, Bohr calculated the energy levels of the hydrogen electron: E n = -.18 x 10-18 J (1/n ) where n is the energy level quantum number. J Energy-Level Diagram ΔE = E f E i = -R H n f -R H n i 1 1 = R H ( ) = h = hc/λ ni n f Note that E H = hcr H, so the Bohr theory allows one to derive the empirical Rydberg Equation Ionization Energy of Hydrogen 1 1 ΔE = R H ( ) = h ni n f Atomic Spectrum Example What is the wavelength of the spectral line resulting from the transitions of an electron from n=5 to n=3 energy level of H? As n f goes to infinity for hydrogen starting in the ground state: 1 h = R H ( ni ) = RH This also works for hydrogen-like species such as He + and Li +. h = -Z R H What is the wavelength of the spectral line resulting from the transitions of an electron from n=5 to n=3 energy level of Li + Z is the charge on the nucleus Bohr Model Example Complete the following table for the radius and circumference of the Bohr electron orbits. H atom n=1 H atom n=3 Li + ion n=1 Li + ion n=3 Radius (pm) Circumference (pm) Bohr Model A summary of the Bohr model: it uses quantum ideas in the form of quantized energy levels for the electron. it explains exactly the line spectrum of hydrogen. it describes electron motion in the atom by hanging on to classical physics (treats electron as an orbiting particle!) while using non-classical assumptions (quantized angular momentum). There are two serious problems with the model: if an electron traveled in an orbit, it would be constantly accelerated and thus radiation should be emitted; it would lose energy and ultimately collapse into the nucleus no stable atoms could exist! it only works for hydrogen like atoms (1 electron atoms) Although fundamentally incorrect it was an important step toward the modern view of the atom. 5

Emission and Absorption Spectroscopy Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality. Einstein suggested particle-like properties of light could explain the photoelectric effect. But diffraction patterns suggest photons are wave-like. debroglie, 194 Small particles of matter may at times display wavelike properties. debroglie and Matter Waves E = mc h = mc h/c = mc = p (c is a velocity) p = h/λ λ = h/p = h/mv (wavelength of a particle) debroglie and Matter Waves Example 1. What is the wavelength of a baseball (145 g) traveling at 150 km/hr?. What is the wavelength of an electron (9.11x10-31 kg) accelerated through 100V? 3. Compare the results to everyday dimensions and atomic dimensions. Evidence of Matter Waves Evidence of Matter Waves Diffraction of light interacting with a periodic structure: this can only be explained by the wavelike behaviour of light. Diffraction patterns arise when the wavelength of light is on the same order as the spacing between points or lines within a periodic structure (e.g. a crystal). From the de Broglie equation, the calculated wavelength of an electron (mass = 9.11 x 10-31 kg) moving at 1.0 x 10 7 m/s (a typical speed of an electron accelerated by an electric field) is 7.7 x 10-11 m. Which is on the order of the distance between atoms within an atomic crystal. So if particles of matter do have wavelike properties, then a beam of electrons should be diffracted by a crystal. This was proved in 197, a diffraction pattern was obtained from a beam of electrons passing through a nickel crystal. Diffraction of slow electrons from a Ni crystal. 6

Werner Heisenberg Δx Δp x The Uncertainty Principle h 4π Wave Mechanics Standing waves. Nodes do not undergo displacement. L λ =, n = 1,, 3 n Introduction to Quantum Mechanics The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus Eψ = H ψ Wave Functions for Hydrogen H(x,y,z) or H (r,θ,φ) e H 4 o r ψ(r,θ,φ) = R(r) Y(θ,φ) R(r) is the radial wave function. Y(θ,φ) is the angular wave function. Quantum Numbers When solving the Schrödinger equation, three quantum numbers are used. Principal quantum number, n (n = 1,, 3, 4, 5, ) Secondary quantum number, ( = 0, 1,,, n - 1) Magnetic quantum number, m (m = -, - + 1, - +,, +) 7

Principle Shells and Subshells Principle electronic shell, n = 1,, 3 Orbital size Quantum Numbers Angular momentum quantum number, = 0, 1, (n-1) Orbital shape = 0, s = 1, p =, d = 3, f Magnetic quantum number, Orbital orientation m = - -, -1, 0, 1, + Note the relationship between number of orbitals within s, p, d, and f and m l. Each principle shell contains n² orbitals. Orbital Energies for 1 Electron Atom En m a n e 0 same as for the Bohr atom Interpreting and Representing the Orbitals of the Hydrogen Atom. Visualizing Orbitals Wave functions for the first five orbitals of hydrogen. The wave function is written in spherical polar coordinates with the nucleus at the origin. Point in space defined by radius r, and angles and. r determines the orbital size. and determine the orbital shape. Visualizing Orbitals A point in space defined by radius r, and angles and. Chemists usually think of orbitals in terms of pictures. The space occupied by an orbital is a 90% probability of finding an electron. A plot of the angular part of the wave function gives the shape of the corresponding orbital. 8

Visualizing Orbitals Visualizing Orbitals An orbital depicts the probability of finding an electron at a given location. Node is a location where the electron is never found (ψ = 0) The radial part of the wave function describes how the probability of finding an electron varies with distance from the nucleus. Spherical nodes are generated by the radial portion of the wave function, R(r). The angular part of the wave function describes how the probability of finding an electron varies with orientation from the nucleus. Nodal nodes are generated by the angular portion of the wave function, Y(θ,φ). s orbitals are spherical p orbitals have two lobes separated by a nodal plane. A nodal plane is a plane where the probability of finding an electron is zero (here the yz plane). d orbitals have more complicated shapes due to the presence of two nodal planes. Probability Distribution for the s Orbitals Radial Probability Distribution for 1s Orbital No spherical nodes 1 spherical node spherical nodes p Orbitals The Boundary Surface Representations of All Three p Orbitals Nodal Plane 9

The Boundary Surfaces of All of the 3d Orbitals Representation of the 4f Orbitals in Terms of Their Boundary Surfaces Orbital Nodes An orbital is description by the quantum numbers n, l and m l Total number nodes (excluding r = 0 and ) is n-1 The number of angular nodes is l whose location depends on the value of m l The number of spherical nodes is n-1- l So for a 4d orbital (n=4, l =) Would have 3 (n-1=3) total nodes; of which (l =) are angular nodes and 1 (n-1- l =1) is spherical node 1 Electron Atomic Orbital Example Which is larger? the H p orbital or the H 3p orbital the H 1s orbital or the Li + 1s orbital Which is lower in energy? the H p orbital or the H 3p orbital a H 4s orbital or a H 4f orbital How many nodes and where are they located in a 4s orbital 3p y orbital 4d xz orbital Electron Spin: A Fourth Quantum Number The spin quantum number, m s, determines the number of electrons that can occupy an orbital. m s = ±1/ Electrons described as spin up or spin down. An electron is specified by a set of four quantum numbers. The Pauli Exclusion Principle The Pauli Exclusion Principle states: No two electrons in an atom can have the same four quantum numbers (n, l, m l, m s ). Two electrons can have the same values of n, l, and m l, but different values of m s. Two electrons maximum per orbital. Two electrons occupying the same orbital are spin paired. 10

Multi-electron Atoms Orbital Energies and Electron Configurations Hydrogen wavefunctions are for only one e - species. Electron-electron repulsion in multi-electron atoms. Use Hydrogen-like orbitals (by approximation). For electrons in larger orbitals, the charge felt is a combination of the actual nuclear charge and the offsetting charge of electrons in lower orbitals. The masking of the nuclear charge is called shielding. Shielding results in a reduced, effective nuclear charge. Penetration and Shielding Z eff is the effective nuclear charge. A Comparison of the Radial Probability Distributions of the s and p Orbitals Effective nuclear charge allows for understanding of the energy differences between orbitals. s orbital: the small local maximum close to the nucleus results in an electron with a higher effective nuclear charge. p orbital: lacks the local minimum close to the nucleus of the s orbital. Lower effective nuclear charge for p electrons. The Radial Probability Distribution of the 3s Orbital A Comparison of the Radial Probability Distributions of the 3s, 3p, and 3d Orbitals 11

The Energies of Orbitals in Polyelectronic Atoms Orbital Energies Aufbau Process As we add protons element by element across the periodic table, electrons are similarly added into hydrogen-like orbitals, starting with the lower-energy orbitals and building up. We can determine the arrangement of electrons (how many electrons in each orbital), called the electron configuration, for all elements on the Periodic Table. We follow two rules to do this 1. We saw that the Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers so only two electrons can be added to each orbital. Orbital Diagram A notation that shows how many electrons an atom has in each of its occupied electron orbitals. Oxygen: 1s s p 4 Oxygen: 1s s p. Hund s Rule states that the lowest energy arrangement of electrons is the one with the maximum number of unpaired electrons (but still following the Pauli Exclusion Principle!) Orbital Filling Ground State Electron Configurations Z Atom Configuration 1s s p 1 3 4 5 6 7 8 9 10 1

Filling the d Orbitals Hund s Rule and the Aufbau Principle The inner electrons, which lie closer to the nucleus, are referred to as core electrons. Core electrons can be represented by the noble gas with the same electronic configuration. The outer electrons are usually referred to as valence electrons. Valence electrons are shown explicitly when a noble gas shorthand is used to write electronic configurations. Valence electrons determine reactivity. Electron Configurations of Some Groups of Elements The Periodic Table and Electron Configurations The periodic table and the electronic configurations predicted by quantum mechanics are related. The periodic table is broken into s, p, d, and f blocks. Elements in each block have the same subshell for the highest electron. Structure of periodic table can be used to predict electronic configurations. The Periodic Table and Electron Configurations Electron Configurations Example For the following chemical species, what are the expected electron configurations. Ca Fe Eu The shape of the periodic table can be broken down into blocks according to the type of orbital occupied by the highest energy electron in the ground state. We find the element of interest in the periodic table and write its core electrons using the shorthand notation with the previous rare gas element. Then we determine the valence electrons by noting where the element sits within its own period in the table. What atom has the following electron configurations? 1s s p 6 3s 3p 5 1s s p 6 3s 3p 6 3d 7 4s 13

Atomic Size Periodic Trends in Atomic Properties Using the understanding of orbitals and atomic structure, it is possible to explain some periodic properties. Atomic size Ionization energy The shell in which the valence electrons are found affects atomic size. The size of the valence orbitals increases with n, so size must increase from top to bottom for a group. The strength of the interaction between the nucleus and the valence electrons affects atomic size. The effective nuclear charge increases from left to right across a period, so the interaction between the electrons and the nucleus increases in strength. As interaction strength increases, valence electrons are drawn closer to the nucleus, decreasing atomic size. Electron affinity Atomic Size Graph showing atomic radius as function of atomic number. Atomic Radii for Selected Atoms Ionization Energy Ionization Energy Ionization energy - the energy required to remove an electron from a gaseous atom, forming a cation. Formation of X + is the first ionization energy, X + would be the second ionization energy, etc. X(g) X + (g) + e - IE 1 X + (g) X + (g) + e - IE Effective nuclear charge increases left to right across a period. The more strongly held an electron is, the higher the ionization energy must be. As valence electrons move further from the nucleus, they become easier to remove and the first ionization energy becomes smaller. Graph of the first ionization energy (in kj/mol) vs. atomic number for the first 38 elements. 14

Ionization Energy Ionization Energy From nitrogen to oxygen, there is a slight decrease in ionization energy. Nitrogen has a half-filled p subshell. Oxygen has a pair of p electrons in one p orbital. Ionization of oxygen relieves electron-electron repulsion, lowering its ionization energy. Ionization energies increase with successive ionizations for a given element. Effective nuclear charge for valence electrons is larger for the ion than the neutral atom. Filled subshells of electrons are difficult to break up, which is why it is difficult to remove electrons from noble gases. The first four ionization energies in kj/mol for elements Z = 1 to 9. Ionization Energy Electron Affinity Electron affinity - energy required to place an electron on a gaseous atom, forming an anion. X(g) + e - X - (g) Electron affinities may have positive or negative values. Negative values - energy released Positive values - energy absorbed Electron affinities increase (numerical value becomes more negative) from left to right for a period and bottom to top for a group. The first four ionization energies in kj/mol for elements Z = 10 to 18. The greater (more negative) the electron affinity, the more stable the anion will be. Electron Affinity Periodic Trends Example Using only the periodic table, rank the following elements O, K, As, S, and Fr. In order of increasing size In order of increasing ionization energy In order of increasing electron affinity Graph of electron affinity (in kj/mol) vs. atomic number for the first 0 elements. 15

Modern Light Sources: LEDs and Lasers Modern Light Sources: LEDs and Lasers Light Emitting Diodes (LEDs) emit monochromatic light. Monochromatic light - light of a single wavelength or color. LEDs are solid-state devices. Simply a piece of solid material. Color emitted depends on identity of solid material. LEDs Metallic leads connect to a piece of semiconductor material. Color emitted is determined by chemical composition of semiconductor. Superior to incandescent lights in efficiency and durability. Modern Light Sources: LEDs and Lasers Lasers emit monochromatic light; color of emitted light depends on chemical composition of laser medium. Lasers emit coherent light; all light waves are perfectly in phase and go through maxima and minima together. Modern Light Sources: LEDs and Lasers Lasers - a direct result of the emergence of the quantum mechanical model of the atom. An understanding of energy levels within the laser medium is needed. Laser operation relies on stimulated emission, where the electron population of higher energy level is greater than a lower energy level. Emission occurs as electrons return to lower energy states. Population inversion in lasers established by solids, liquids or gases. Solid-state lasers are used in electronics. Lasers Light Amplification by Stimulated Emission of Radiation (LASER) Modern Light Sources: LEDs and Lasers Bright blue light emitted by an organic light emitting diode (OLED). Holds promise of an entirely new class of paper-thin flexible color displays. 16