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Electrons as waves • Scientists accepted the fact that light has a dual wave- particle nature. • De Broglie pointed out that in many ways the behavior of the Bohr’s quantized electron orbits was similar to the known behavior of waves. • Electrons should be thought of as having a dual wave-particle nature also. Evidence; Electrons • Electron beams could be diffracted or bent. • Electron beams demonstrated the properties of interference. Heisenberg Uncertainty Principle • Werner Heisenberg (1927) • It is impossible to determine simultaneously both the position, and velocity, of an electron or any other particle. Heisenberg explained • To locate an object you would have to be able to look at it. • When we see an object we actually are seeing the light waves that the object reflects. • For us to see an object a photon of light has to hit it. Heisenberg explained • A photon hitting a book or an airplane has no noticeable affect. • However, an electron is so small that once a photon its it, the electron undergoes a large energy change and is moved. • Similarly, the collision between the photon and the electron causes the electrons velocity to change. In summary • If we were able to measure the location, the velocity would change • If we were to measure the velocity, the location will change. • Note: Treats electron like a particle Schrodinger ‘s wave equation • Developed an equation that treats electrons as waves. ( related the amplitude of the electron wave to any point in space around the nucleus). Quantum theory • Heisenberg’s uncertainty principle and Schrodinger’s equation laid the foundation for quantum theory. • Quantum theory- describes mathematically the wave properties of electrons and other very small particles. Probability • Ceiling fan- where are the blades at any one moment? Orbital • Three dimensional region around the nucleus that indicates the probable location of an electron. • These three dimensional shapes are named s, p, d, and f. • When describing the location of the electrons in an orbital we are indicating that there is a 99 % chance that the electron will be found there. Quantum numbers • A list of three numbers that describe the location of the electron • The numbers represent – The main energy level – The shape – The orientation of the orbital, axis Spin of electron • A fourth number indicates the spin within the orbital. Principle quantum number • 1-7 representing the energy level • Symbolized by the letter n • As n increases the distance from the nucleus increases • As n increases the potential energy of the electron increases. Angular momentum or orbitals • The different shaped orbitals are also called sublevels. • Symbolized by l, indicates the shape of the orbital • 2 electrons are allowed in one orbital • The number of orbital shapes, l, possible is equal to n ( up to n=4) continued • The values of l allowed are 0 and all possible integers up to n-1 • l= n-1 0 = s shape 1 = p shape 2 = d shape 3 = f shape 2 electrons per orbital • • • • The s shape has 1 orbital – total of 2 electrons The p shape has 3 orbitals – 6 electrons The d shape has 5 orbitals – 10 electrons The f shape has 7 orbitals – 14 electrons • See page 103 • Each orbital is on a different axis, ( x,y,z etc. ) Magnetic quantum number • Indicates the orientation of the orbital around the nucleus. • Symbolized by the letter m • Indicated by numbers on either side of zero • The s shape has an m value of 0 ( no axis) • The p shape has m values of –1,0,+1 • The d shape has m values of –2,-1,0,+1,+2 Summary • n,l,m • Energy level, shape, axis Spin The last number is a spin indicator • -1/2 or + ½ • These are the two spin states, ( spin to the right or spin to the left) • No two electrons can be identical., or , no two electrons can have the same set of quantum numbers – Pauli’s exclusion principle • A maximum of two electrons can occupy an orbital, each will have a different spin. Mathematical equations • The number of orbitals per energy level is n2 n=2, there are 4 orbitals; 1 s and 3 p n=3 there are 9 orbitals; 1s, 3p, 5d Number of electrons • Since there are 2 electrons per orbital • 2n2 is the number of electrons per energy level.