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 n 2 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 2n 2 is the number of electrons per energy level.