1. Quantum theory Electron Clouds and Probability

2. 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=mc 2 ) with Plank’s quantum equation (E= hv) (Plank’s constant, frequency of a wave) mc 2 = hv substitute c with v ( general velocity) v(frequency of wave)= v /  velocity/wavelength)

3. Final equation = h m v 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

4. Momentum (p) is the product of mass and velocity (speed and direction of motion = h/p  Wavelength inversely proportional to momentum  Only worth studying for particles of small mass  Quantum mechanic: small particles traveling near speed of light

5. 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

6. 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

7. 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

8. 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

9. 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 e - is most likely to be found

10. Since the e - is traveling at the speed of light and appearing at all these positions, the e - appears 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

11. 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

12. 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)

14. 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.htmlhttp://www.colorado.edu/physics/2 000/applets/a2.html

15. 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

16. 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 2n 2

17. 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

18. 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 2 nd sublevel is p so 2 nd level has an s and p 3 rd sublevel is d so 3 rd has a s,p,d 4 th sublevel is f so 4 th has s,p,d,f

19. 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)

20. 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

21. 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:

23. 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  used to show spin direction Pauli Exclusion Principle: no two e- in the same atom can have the exact same four quantum values

24. 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:.

25. 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

27. 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.

29. 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.