* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Quantum theory
Quantum group wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Coherent states wikipedia , lookup
Wave function wikipedia , lookup
Renormalization group wikipedia , lookup
Quantum key distribution wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Tight binding wikipedia , lookup
Bell's theorem wikipedia , lookup
Renormalization wikipedia , lookup
Elementary particle wikipedia , lookup
Franck–Condon principle wikipedia , lookup
Identical particles wikipedia , lookup
Hidden variable theory wikipedia , lookup
Quantum teleportation wikipedia , lookup
History of quantum field theory wikipedia , lookup
EPR paradox wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Quantum state wikipedia , lookup
Canonical quantization wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Double-slit experiment wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Probability amplitude wikipedia , lookup
Particle in a box wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Matter wave wikipedia , lookup
Wave–particle duality wikipedia , lookup
Hydrogen atom wikipedia , lookup
Atomic theory wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Quantum theory Electron Clouds and Probability • Bohr’s model of the atom is unable to describe electron (e-) behavior in an atom • Problem: multiple spectral lines closely spaced • deBroglie Hypothesis • Believed e- had a Dual-nature • Acted as particles with mass and waves of energy with no mass, simultaneously • Combined Einstein’s Relativity equation (E=mc2) with Plank’s quantum equation (E= hv) (Plank’s constant, frequency of a wave) • mc2 = hv substitute c with v ( general velocity) • v(frequency of wave)= v/l velocity/wavelength) • Final equation l = h mv • Enabled de Broglie to predict the wavelength of a particle of mass m and velocity v • Showed that an e- stream acted as a group of particles and in some ways as a ray of light • Waves can act as particles and particles can act as waves • Wave-particle duality of nature • Momentum (p) is the product of mass and velocity (speed and direction of motion l = h/p Wavelength inversely proportional to momentum Only worth studying for particles of small mass Quantum mechanic: small particles traveling near speed of light • Heisenberg studied e- as particles • Noted it was impossible to determine both the exact position and exact momentum of an e- at the same time • Due to the fact that you interacted with the particle to “see” it and changed one of the two properties • There is always uncertainty • Proposed Heisenberg Uncertainty Principle • Impossible to know the exact position and momentum of an e- at the same time • Scientists are unable to describe the exact structure of an atom due to this • But it can be determined with probability • Can determine with high probability where an e- is most likely to be found in the energy levels of an atom at any one given time • Schrodenger • Studied e- as waves • Found amplitude of wave was related to distance or point in space an e- was from the nucleus • Developed an equation using e- energies and amplitude along with quantum levels to describe wave function • Included e- total and P.E. in equation • Max Born found that the square of the amplitude gave the probability of finding the e- at that same point in space around the nucleus for which the equation is solved • Probability • Is the ratio between the number of times the e- is in that current position and the total number of times it is at all positions • The higher the probability, the more likely the e- will be found in a given position • The probability plots give a three dimensional shape to a region of space an eis most likely to be found • Since the e- is traveling at the speed of light and appearing at all these positions, the eappears to be everywhere • The area the e- occupies appears to be a region of negative charge with a specific shape • This is referred to as an Electron cloud • Now lets put this into the Bohr Model • Electrons are assumed to have a circular path and to always be found at a specific distance from the nucleus dependent on their P.E.(ground state) • But there is the probability of any e- at trillions if not more points in space • Many of these points have high probability • Connect all these points together and you obtain a 3D shape • The most probable place to find the e- is on the surface of this shape • Remember that e- move near speed of light • The e- random movement causes it to appear as a cloud • The e- occupies all the volume of this cloud • Does not normally go beyond the outer volume area(ground state) • Now in order to describe an e- behavior we need to represent different energy states • Do this by use of quantum numbers • The differences correspond to the lines observed in the spectrum of atoms • Easily described using H • When an e- moves from ground to excited state, energy emitted as a form of light • Represented by a line in the H spectrumhttp://www.colorado.edu/physics/2 000/applets/a2.html • Atoms with more than one e• Interactions of the other e- cause other problems as well as the increased nuclear pull • It is assumed that the various e- in a multielectron atom occupy the same energy states without affecting each other • To describe an e- in an atom, four quantum numbers are required • Quantum numbers are ID’ed by the letters n, l, m, s • Each e- has its own unique set of these four numbers • Any one e- can occupy only a specific energy level based on its total and P.E. • These energy levels are represented by whole integers starting with 1 • The number of the energy level, represented by the letter n, is called the Principle Quantum Number 1,2,3….n • Electrons can be found in each energy level of an atom • Greatest number of e- in a level is 2n2 • Second Quantum number is l • Represents the energy sublevels and orbitals • Each energy level is a group of energy states • Represented by the number of spectral lines we saw of the same color • These are closely grouped together • States called sublevels • # sublevels in an energy level is equal to the principle quantum number • • • • • Principle quantum level 1 has 1 sublevel Principle quantum level 2 has 2 sublevels Principle quantum level 3 has 3 sublevels And so on… The lowest sublevel of energy in any principle energy is always designated by the letter s • 2nd sublevel is p so 2nd level has an s and p • 3rd sublevel is d so 3rd has a s,p,d • 4th sublevel is f so 4th has s,p,d,f • Each sublevel holds a maximum number of e• Every s can contain 2e- (one pair) • Every p can contain 6e- (three pair) • Every d can contain 10e- (five pair) • Every f can contain 14e- (seven pair) • Each pair in a sublevel has a different place in space • Due to the interactions of the e- within a sublevel on each other • Try to be as far from each other as possible due to the fact they are all same charge • The space occupied by one pair of e- is called an orbital • Designated by quantum number m • Defines each orbital by indicating its direction in space • Ex. Sublevel s is simply spherical in nature • Sublevel p with three orbitals (6e-, 3 pairs) has e- in 3D along the x,y,z axis • Orbitals of the same sublevel are alike in size and shape and have same energy • Orbitals of the same energy are called DEGENERATE • Shapes: • • • • Electrons in the same orbital must coexist together How if they are repulsive Fourth quantum number is spin s Electrons in the same orbital spin in opposite directions • Sets up opposite magnetic fields, so e- become slightly attractive to each other • Up and down arrows E used to show spin direction • Pauli Exclusion Principle: no two e- in the same atom can have the exact same four quantum values • So lets see how e- would start to occupy positions in an atom • Aufbau principle states that e- will always occupy lowest available energy levels first • So lets see how this might look: • . • As more e- are added to the atom and occupy higher energy levels, the interactions become greater between e- of different energy levels and sublevels • Also remember that the nucleus is also gaining protons and its overall charge is increasing causing it to pull harder • All these interactions force sublevels to begin to overlap each other • It changes the filling pattern of e- in atoms • Note: starting with energy level three, 4s fills before 3d • Thus have a new filling pattern for e• Can use an ARROW DIAGRAM to determine the pattern • . • One more e- filling fact • Hund’s Rule: • The most stable atoms are those which have the most parallel (same direction) spinning e• Designated by using boxes and the arrows for e- spin • .