Wave-Particle Duality Louis De Broglie (1924) Proposed that ALL matter has wave and particle properties, not just electrons. E = E E = hυ or E = hc/λ & E = mc2 hc/λ = mc2 hc = mc2λ h = mcλ λ = h/mc OR λ = h/mv Example: λ of baseball (mass = .2 kg and v = 30 m/s) λ of an electron (mass = 9.11 x 10-31 kg and v = 3 x 108 m/s)
Wave Mechanical Model Schroedinger (1887-1961) Developed the “wave mechanical model” of the atom (also known as the quantum mechanical model) He used the following equation to produce scatterplots that are now called “electron clouds” E = 22me2/h2n2 These electron clouds are areas in which there is a great probability of finding an electron (90%). The cloud is more dense where the probability of finding an electron is high. The cloud is less dense where the probability of finding an electron is low. This is called an “orbital” – a region in space in which there is a high probability of finding an electron.
http://scienceworld.wolfram.com/physics/SchroedingerEquation.html http://www.uark.edu/misc/julio/orbitals/index.html
Is That It? - Uncertainty Heisenberg (1927) Said that because of size and speed it is impossible to know both exact position and momentum of and electron at the same time. This is referred to as the “Heisenberg Uncertainty Principle” To “see” an electron we strike it with something of similar size and observe its behavior. We cannot see an electron directly. We use photons of energy to do this.
Quantum Mechanics The work of de Broglie, Schroedinger, Born, and Heisenberg led to the study of “quantum mechanics” and the “wave mechanical model” 1. classical physics describes the motion of bodies much larger than the atoms of which they are composed. energy can be gained or lost in any amount 2. quantum physics describes the motion of atoms and subatomic particles as waves. particles gain or lose energy in packets called “quanta”
Energy Components in Electrons Each component is given a letter & a name – we call them “quantum values” 1. n = principal distance from the nucleus 2. l = azimuthal angular momentum 3. m = magnetic interaction with electromagnetic fields 4. s = spin axial rotation Using these we can pinpoint the location of an e-.
Location n = principal energy level (shell) n + l = energy sublevel (subshell); defines the type of orbital that the electron is in n + l + m = specific orbital (axis orientation) n + l + m + s = spin (exact electron), identifies the exact electron and its location ANALOGY
Orbital Types S-orbital = spherical shape, only 1 of them P-orbital = gumdrop or dumbell shape, 3 of them – one on each axis (x,y,z) D-orbital = donut shape, 5 of them F-orbital = cigar shape, 7 of them Each orbital contains a max of 2 electrons Orbit – path of an electron (according to Bohr) Orbital – region in space where there is a high probability of finding an electron
ENERGY LEVELS ORBITAL TYPES # OF ORBITALS # OF ELECTRONS n = 1 s 1 2 n = 2 s,p 4 8 n = 3 s,p,d 9 18 n = 4 s,p,d,f 16 32 n = 5 s,p,d,f,”g” 25 50 Energy level = the number of orbital types Total number of orbitals in an energy level = n2 Total number of electrons in any energy level = 2n2