The Quantum Model Chapter 4

Electrons as Waves & Particles Where do electron’s exist? How can you find the exact location and position of one, individual electron? Electrons are detected by their interaction with photons They have the same energy, so any attempt to locate an e- with a photon knocks the e- off its course. Heisenberg Uncertainty Principle: impossible to determine simultaneously both the position and velocity of an electron or any other particle

Schrodinger Wave Equation Schrodinger hypothesized that e-’s have both a dual wave-particle nature Quantum Theory: describes mathematically the wave properties of electrons and other very small particles Gives the probability of finding an electron at a given place around the nucleus Orbitals: suggested that e-’s exist here instead of defined orbits

Think of a US map listing all the different zip codes and their locations - Merely #’s that refer to the positions of different postal zones Just like an atom, quantum numbers, depict positions, and therefore energy levels of different e-’s in the atom. Notice that no two postal codes are the same, neither does an atom have the same set of quantum numbers.

Principle Quantum Number Referred to as n -has integral values of 1, 2, 3,…. -as n increases, the orbital gets larger Sometimes referred to as shells -as n increases, more time is spent away from the nucleus. -as n increases, the e- has a higher energy

N contains a certain # of sublevels Example: So if n = 2, it contains two sublevels, s and p Value of n 1 2 3 4 Type of sublevels s s,p s, p, d s, p, d, f

Angular Momentum (Azimuthal) Quantum # Symbolized by L -has integral values from 0 to n – 1. -defines the shape of the orbital -the value of L for each orbital is designated by the letters, s, p, d, & f, which correspond to the values of 0, 1, 2, 3 Value of L 1 2 3 Letters Used s p d f

Magnetic Quantum Number Symbolized by mL Example: has integrals values between L and - L, including 0. describes the orientation of the orbital in space Example: L = d there are five different orientations that correspond to the values, -2, -1, 0,1, 2

Spin Quantum Number Symbolized ms Only two possible values, + ½ & - ½ Orbital can hold a maximum of two electrons, which must have opposite spins

Electron Configuration This is the arrangement of electrons in an atom Rules that must be followed: Aufbau Principle: an e- occupies the lowest orbital that can receive it. Pauli Exclusion Principle: no 2 e-’s in the same atom can have the same set of quantum #’s Hund’s Rule: orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and they must have parallel (same) spins

Grab your periodic tables from and your colored pencils.

Electron Configuration 1. The arrangement of electrons in an atom. 2. Electrons like to assume arrangements in their ground states, because they want the lowest possible energy. 3. The electron configuration can be described pictorially drawn denotes the number of electrons in orbital or subshell 1s1 denotes n denotes l The orbital diagram that shows the spin of the electron is:

Noble Gas Notation: Example Mg: [Ne]3s2 Electron Configuration Noble Gas Notation Orbital Diagram Excited State vs. Ground State Ions in Electron configuration, noble gas notation, and orbital diagrams Cr vs Cu Isoelectronic

Valence electrons & Lewis dot structures Valence electrons are the outermost s and p electrons. Can never be more than 8. These are the electrons used in bonding!!! Lewis dot structures show the distribution of valence electrons. Also can’t be more than 8.

Properties of Light Light: a form of radiant energy consisting of electromagnetic waves that travel freely through space Electromagnetic radiation: form of energy that exhibits wavelike behavior as it travels through space All forms of electromagnetic radiation form the electromagnetic spectrum

Wavelength, Frequency & Energy Visible Light Features: Wavelength, Frequency & Energy Light have wave-like properties as described by visible light. The electromagnetic spectrum illustrates the wave properties of light

Wavelength & Frequency Wavelength:  distance between corresponding points on adjacent waves Frequency:  the number of waves that pass a given point in a specific time, usually one second

Relating frequency and wavelength Use the equation to relate frequency and wavelength  is inversely proportional to , so in other words as the wavelength of light decreases, its frequency increases or vice versa. = ln c

The Photoelectric Effect Refers to the emission of electrons from a metal when light shines on the metal.

Light as Particles E = h v where h = 6.626 x 10-34 J s Planck proposed that objects emitted energy in small, specific amounts called quantum. This is the amount of energy that can be lost or gained by an atom Planck suggested a relationship between a quantum of energy and the frequency of radiation Light has particle like properties as described by the photoelectric effect which is the emission of an electron from a metal when light strikes it E = h v where h = 6.626 x 10-34 J s

Light having a dual wave-particle like nature Einstein expanded on Planck’s theory by introducing the concept of light have a dual wave-particle like nature Each particle of light carries a quantum of energy, called photons Ephoton = hv Putting Einstein and Planck together E = mc2 E= hc/ Solve For m mc2 = hc/ mc = h/  (1/c) mc2 = hc/  (1/c) (1/c) mc = h/  (1/c) (1/c) mc2 = hc/  (1/c) m = h c

Continuous Spectrum vs. Line Spectrum Continuous Spectrum: when white light is passed through a prism and all the wavelengths of visible light are seen. Line Spectrum: when the emission spectrum of a certain gas is passed through a prism, only bands of certain wavelengths are seen.

Hydrogen-Atom Line Emission Spectrum Passed current through a tube containing hydrogen gas Narrow beam of light passed through prism and a series of frequencies or wavelengths were seen.

Scientists figured that since only specific frequencies of light were emitted then the energy differences between the atoms’ energy were fixed. This is what lead Bohr to believe that a hydrogen atom exists only in very specific energy states

These are additional lines that were discovered in the ultraviolet and infrared regions of hydrogen’s line spectrum

What Bohr Proposed 1. The electron on the hydrogen atom can exist only in certain spherical orbits. 2. As the distance from the nucleus increases, the energy of an electron in that orbit increases. 3. The closest orbit (energy level) is called the ground state. Higher energy levels are called excited states. 4. When an electron falls from a higher energy level to a lower energy level, it emits a definite amount of energy that is equal to the difference in the energy of the two levels.

Bohr’s Model Ephoton = energy of level nfinal -energy of level ninitial