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CHAPTER 11 NOTES MODERN ATOMIC THEORY RUTHERFORD’S MODEL COULD NOT EXPLAIN THE CHEMICAL PROPERTIES OF ELEMENTS The Bohr Model • Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus • Energy Levels – the fixed energies an electron can have – like rungs of a ladder • Quantum – the amount of energy required to move an electron from one energy level to another energy level • Quantum Mechanical Model – the modern description of the electron in atoms – from the mathematical solutions to the Schrödinger equation – determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus ATOMIC ORBITALS • Atomic orbital – a region in space in which there is a high probability of finding an electron • Different atomic orbitals are denoted by letters. s Orbitals p Orbitals d Orbitals f Orbitals g Orbitals • Each energy sublevel corresponds to an orbital of different shape describing where the electron is likely to be found Hydrogen Energy Levels • The s and p types of sublevel Principal Quantum Numbers • (n) – always equals the number of sublevels within that principal energy level Principal Energy Level # of Sublevel s Type of Sublevel s Max # of Electrons n=1 1 1s 2 n=2 2 2s,2p 8 n=3 3 3s,3p,3d 18 n=4 4 4s,4p,4d, 32 4f n=5 5 5s,5p,5d, 50 5f,5g n=6 5 6s,6p,6d, 50 6f,6g n=7 2 7s,7p 8 ELECTRON CONFIGURATIONS • • Electron Configurations – the ways in which electrons are arranged into various orbitals around the nuclei of atoms 3 RULES AUFBAU PRINCIPLE • ELECTRONS OCCUPY THE ORBITALS OF LOWEST ENERGY FIRST PAULI EXCLUSION PRINCIPLE • AN ATOMIC ORBITAL MAY DESCRIBE AT MOST 2 ELECTRONS HUND’S RULE • ELECTRONS OCCUPY ORBITALS OF THE SAME ENERGY IN A WAY THAT MAKES THE NUMBER OF ELECTRONS WITH THE SAME SPIN DIRECTION AS LARGE AS POSSIBLE EXAMPLE I o Element = SODIUM o Element Symbol = Na o ATOMIC NUMBER = 11 o NUMBER OF ELECTRONS = 11 o LONG-HAND VERSION 1s2 2s2 2p6 3s1 EXAMPLE I continued • SHORT-HAND VERSION 1s22s22p63s1 • NOBLE GAS CONFIGURATION [Ne]3s1 EXAMPLE II o Ion Name = SODIUM ION o Ion Symbol = Na+ o ATOMIC NUMBER = 11 o NUMBER OF ELECTRONS = 10 o LONG-HAND VERSION 1s2 2s2 2p6 EXAMPLE II continued • SHORT-HAND VERSION 1s22s22p6 • NOBLE GAS CONFIGURATION [Ne] EXCEPTIONAL ELECTRON CONFIGURATIONS • MEMORIZE THE FOLLOWING Cr, Cu, Mo, Pd, Ag and Au • Some actual electron configurations differ from those assigned using the Aufbau Principle because half-filled sublevels are not as stable as filled sub-levels, but they are more stable than other configurations • Transition metals usually lose s orbital electrons first. EXAMPLE I • • • • Element Name = Chromium # of Electrons = 24 Short-Hand Version = 1s22s22p63s23p64s13d5 Noble Gas Configuration = [Ar] 4s13d5 EXAMPLE II • • • • Element Name = Copper # of Electrons = 29 Short-Hand Version = 1s22s22p63s23p64s13d10 Noble Gas Configuration = [Ar] 4s13d10 • Transition metal ions having partially filled d orbitals usually have a color. • Transition metals usually lose s orbital electrons first. • Example A: Fe and Fe3+ • Fe (26 electrons) - 1s22s22p63s23p64s23d6 • Fe3+ (23 electrons) - 1s22s22p63s23p63d5 • Example B: Cu and Cu2+ • Cu (29 electrons) - 1s22s22p63s23p64s13d10 • Cu2+ (27 electrons) - 1s22s22p63s23p63d9 Physics and the Quantum Mechanical Model • Amplitude – wave’s height from zero to the crest • Wavelength (λ) – the distance between the crests • Frequency (ν) – the number of wave cycles to pass a given point per unit of time SI unit of frequency is a hertz (Hz) or expressed as a reciprocal second (s-1 or 1/s) • c = λν • The wavelength and frequency of light are inversely proportional to each other • c = speed of light (3E8 m/s or 3 E10 cm/s) • When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels. • • • • E E h ν = = = = hν energy measure in Joules (J) Planck’s Constant = 6.6262E-34 Js frequency (s-1) • • • • • E E h c λ = = = = = hc/λ energy measure in Joules (J) Planck’s Constant = 6.6262E-34 Js speed of light = 3E8 m/s wavelength measured in meters (m) • • • • • λ = h/mv λ = wavelength measured in meters (m) h = Planck’s Constant = 6.6262E-34 Js m = mass measured in kilograms (kg) v = velocity measured in meters per second (m/s) EXAMPLES • WHAT IS THE FREQUENCY OF RADIATION WHOSE WAVELENGTH IS 550 NM? • WHAT IS THE ENERGY (IN J) OF A PHOTON WHOSE FREQUENCY IS 3.2 E 14 HZ? • WHAT IS THE WAVELENGTH (IN NM) OF RADIATION WITH A FREQUENCY OF 6.50E14 S-1? Electromagnetic Spectrum • Atomic emission spectrum – frequencies of light emitted by an element that separate into discrete lines • Ground State – lowest possible energy of an electron (n = 1). Excitation of the electron by absorbing energy raises it from the ground state to an excited state (n = 2,3,4,5,6 or 7) • The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron • Heisenberg uncertainty principle – it is impossible to know exactly both the velocity and the position of a particle at the same time. Atoms can give off light. They first must receive energy and become excited. The energy is released in the form of a photon. The energy of the photon corresponds exactly to the energy change experienced by the emitting atom. • Atomic states Excited state – atom with excess energy Ground state – atom in the lowest possible state • When an H atom absorbs energy from an outside source it enters an excited state. Quantized Energy Levels • Since only certain energy changes occur the H atom must contain discrete energy levels. Quantized Energy Levels • The energy levels of all atoms are quantized.