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 = 111s2 n = 222s,2p8 n = 333s,3p,3d18 n = 444s,4p,4d, 4f 32 n = 555s,5p,5d, 5f,5g 50 n = 656s,6p,6d, 6f,6g 50 n = 727s,7p8

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 oElement = SODIUM oElement Symbol = Na oATOMIC NUMBER = 11 oNUMBER OF ELECTRONS = 11 oLONG-HAND VERSION 1s 2 2s 2 2p 6 3s 1

EXAMPLE I continued SHORT-HAND VERSION 1s 2 2s 2 2p 6 3s 1 NOBLE GAS CONFIGURATION [Ne]3s 1

EXAMPLE II oIon Name = SODIUM ION oIon Symbol = Na + oATOMIC NUMBER = 11 oNUMBER OF ELECTRONS = 10 oLONG-HAND VERSION 1s 2 2s 2 2p 6

EXAMPLE II continued SHORT-HAND VERSION 1s 2 2s 2 2p 6 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 = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 Noble Gas Configuration = [Ar] 4s 1 3d 5 EXAMPLE II Element Name = Copper # of Electrons = 29 Short-Hand Version = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 Noble Gas Configuration = [Ar] 4s 1 3d 10

Transition metal ions having partially filled d orbitals usually have a color. Transition metals usually lose s orbital electrons first. Example A: Fe and Fe 3+ Fe (26 electrons) - 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 Fe 3+ (23 electrons) - 1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 Example B: Cu and Cu 2+ Cu (29 electrons) - 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 Cu 2+ (27 electrons) - 1s 2 2s 2 2p 6 3s 2 3p 6 3d 9

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 = hν E = energy measure in Joules (J) h = Planck’s Constant = E-34 Js ν = frequency (s -1 ) E = hc/λ E = energy measure in Joules (J) h = Planck’s Constant = E-34 Js c = speed of light = 3E8 m/s λ = wavelength measured in meters (m)

λ = h/mv λ = wavelength measured in meters (m) h = Planck’s Constant = E-34 Js m = mass measured in kilograms (kg) v = velocity measured in meters per second (m/s)

EXAMPLES W HAT IS THE FREQUENCY OF RADIATION WHOSE WAVELENGTH IS 550 NM ? W HAT IS THE ENERGY ( IN J ) OF A PHOTON WHOSE FREQUENCY IS 3.2 E 14 HZ ? W HAT 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.