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### C H6

1. 1. CHAPTER 6 ELECTRONIC STRUCTURE OF ATOMS
2. 2. The Wave Nature of Light <ul><li>All radiated energy can be thought of as a wave </li></ul><ul><li>The waves are electromagnetic in nature (they are caused and effected by both electrical charge and magnetic fields) </li></ul><ul><li>All these waves travel at the same speed, the speed of light (which is an electromagnetic radiation) </li></ul>
3. 3. <ul><li>The distance from the top of one wave to the top of the next one is the wavelength </li></ul><ul><li>The number of waves that pass a point each second is the frequency </li></ul><ul><li>The height of the wave is the amplitude </li></ul>The Wave Nature of Light
4. 4. <ul><li>The Electromagnetic Spectrum lists the “names” of different types of waves by their wavelength and frequency </li></ul>The Wave Nature of Light
5. 5. <ul><li>From the last picture, it is obvious that wavelength and frequency are related </li></ul><ul><li>Remember that all emag waves travel at the same speed </li></ul><ul><li>At the same speed, the waves with less distance to travel pass by my point more often. </li></ul><ul><li>The equation for frequency ( ν ) and wavelength ( λ ) is </li></ul><ul><li>c= ν * λ </li></ul><ul><li>Frequency is measured in Hertz (s -1 ) </li></ul>The Wave Nature of Light
6. 6. <ul><li>Did you grandmother or mother ever say “Don’t touch that stove it’s red hot!”? </li></ul><ul><li>When you take something and heat it up it, at some high temperature it will start to give off visible light, red to start. </li></ul><ul><li>This is called black body radiation since the thing was black when we started. </li></ul><ul><li>The question is how much energy is given off at a specified temperature? </li></ul>Quantized Energy & Photons
7. 7. <ul><li>Normally, the energy given off is thought of as a bell curve, with there being tiny amounts of high energy (high frequency) waves, more and more middle energy waves, and tiny amounts of low energy waves. </li></ul>Quantized Energy & Photons
8. 8. <ul><li>X represents the average wavelength given off, and notice how the wave lengths should tapper off as they get larger and smaller. </li></ul><ul><li>What’s the problem with this? </li></ul>Quantized Energy & Photons
9. 9. <ul><li>The bell curve NEVER reaches 0. </li></ul><ul><li>The area under the curve is infinite since it keeps going. </li></ul><ul><li>The area under the curve represents the total energy given off. </li></ul><ul><li>Objects DO NOT each give off infinite amounts of energy. </li></ul><ul><li>So what is really happining? </li></ul>Quantized Energy & Photons
10. 10. <ul><li>Enter Max Plank </li></ul><ul><li>His theory is that energy can only be given off in “pieces” of a minimum (whole number) amounts. </li></ul><ul><li>In Latin, the word the word for fixed amount is QUANTUM. </li></ul><ul><li>Now, when we get to the right of the bell curve, you reach a point where the object does not have enough energy left to emit another stronger quanta. </li></ul><ul><li>The object no longer emits infinite energy </li></ul>Quantized Energy & Photons
11. 11. <ul><li>Plank proposed that the energy of any quanta is equal to it’s frequency time a constant: </li></ul><ul><li>E=hv </li></ul><ul><li>h is called Plank’s constant and </li></ul><ul><li>h=6.626x10 -34 Js (joule seconds) </li></ul>Quantized Energy & Photons
12. 12. <ul><li>According to Plank’s theory, energy can only be emitted in whole number multiples of hv (hv, 2hv, 3hv, …). </li></ul><ul><li>Now, I know I said light can be thought of as a wave ten slides ago, but now let’s think of it a a particle, called a photon. </li></ul><ul><li>The energy of the photon is given by Plank’s law E=hv </li></ul><ul><li>Plank’s law can be written for wave length since v=c/ λ  E=hc/ λ </li></ul>Quantized Energy & Photons
13. 13. <ul><li>Now let’s look a an electron orbiting an atom. </li></ul><ul><li>The electron is held on by a fixed amount of energy (it were held infinitely tight, there could be no sharing or transfer of electrons needed for chemical reactions) </li></ul><ul><li>If the electron is hit by a photon with more energy then the atom is holding it by, the electron is ejected from the atom. </li></ul>Quantized Energy & Photons
14. 14. <ul><li>When a photon bumps an electron out of an atom it is called the photoelectric effect. </li></ul><ul><li>This is how solar cells work. </li></ul><ul><li>Metals are usually the only atoms that give off electrons. </li></ul><ul><li>Each metal has a different minimum energy (more to follow) </li></ul>Quantized Energy & Photons
15. 15. <ul><li>If you shine a white light through a prism a full spectrum is generated </li></ul>Line Spectra & the Bohr Model
16. 16. <ul><li>If you shine a lamp made with an elemental gas (neon) or vaporized element through a prism, only a few lines are generated. </li></ul><ul><li>These are called Spectral Lines </li></ul>Line Spectra & the Bohr Model
17. 17. Line Spectra & the Bohr Model <ul><li>Rydberg figured out an equation to relate the 4 lines of the hydrogen spectrum: </li></ul>
18. 18. <ul><li>Why don’t electrons “fall” into the nucleus of an atom? Bohr came up with a model of the atom that explained this and the spectral lines: </li></ul><ul><li>Only electron orbits of certain radii (corresponding to definite energies) are allowed. </li></ul><ul><li>Electrons in an allowed orbit will not radiate energy (so they can’t spiral into the nucleus). </li></ul><ul><li>Energy is only absorbed or emitted when electrons move from one allowed orbit to another. The energy is emitted as a photon, E=hv </li></ul>Line Spectra & the Bohr Model
19. 19. <ul><li>Bohr combined the equation for motion, electrical charges, and emission energy, and came up with: </li></ul><ul><li>E=(-hcR h )(1/n 2 ) </li></ul><ul><li>H is Planks constant, R h is Rhdberg’s constant, and c is the speed of light so if we put those numbers in we get: </li></ul><ul><li>E=-2.18*10 -18 (1/n 2 ) J </li></ul><ul><li>n is a number from 1 to ∞ called the quantum number </li></ul>Line Spectra & the Bohr Model
20. 20. <ul><li>E=-2.18*10 -18 (1/n 2 ) </li></ul><ul><li>When n=1 (the smallest it can be) the electron is in the ground state, and </li></ul><ul><li>E=-2.18*10 -18 J </li></ul><ul><li>What happens when the electron moves infinitely far away? (1/n 2 ) becomes 0 so E=0. This is called the zero energy state (really imaginative name) </li></ul>Line Spectra & the Bohr Model
21. 21. <ul><li>Why is the lowest (ground) state negative and the highest zero? </li></ul><ul><li>Higher orbits have greater energy </li></ul><ul><li>Electrons “want” to be close to nuclei </li></ul>Line Spectra & the Bohr Model
22. 22. <ul><li>What happens if an electron absorbs energy and gets “bumped” up to a higher energy level? </li></ul><ul><li>The electron is in a high energy state, but things like to be in the lowest energy state, so it gives off the energy according to the emission rules </li></ul>Line Spectra & the Bohr Model
23. 23. Line Spectra & the Bohr Model
24. 24. <ul><li>Limitations of the Bohr model: </li></ul><ul><li>It only explains the spectral lines of Hydrogen </li></ul><ul><li>Saying the electron won’t fall into the nucleus because it can’t isn’t good enough </li></ul><ul><li>So thinking of an electron as a planet circling a sun is not that good of an idea </li></ul><ul><li>Where have you heard that before? </li></ul>Line Spectra & the Bohr Model
25. 25. <ul><li>Wave – Particle; Particle – Wave: which is it all ready!!!! </li></ul><ul><li>Well either or both, don’t ask me why </li></ul><ul><li>Try reading In Search of Schrodinger's Cat: Quantum Physics And Reality by John Gribin sometime. </li></ul><ul><li>Short answer, if you look for a wave, you find a wave, if you look for a particle, you find a particle. </li></ul>Wave Behavior of Matter
26. 26. <ul><li>New guy De Broglie decides to look at electrons as waves. </li></ul><ul><li>The electron would have a wavelength </li></ul><ul><li>De Broglie proposed that the wavelength depended on the mass and velocity of the electron: </li></ul><ul><li>Λ =h/mv </li></ul><ul><li>mv for any object is it’s momentum </li></ul><ul><li>ANY object has a wavelength, even you and I, but our wavelength is too small to observe </li></ul>Wave Behavior of Matter
27. 27. <ul><li>The uncertainty principle – Heisenberg </li></ul><ul><li>If I roll a bowling ball down a ramp, I can measure it’s position and velocity at any time. I know these things because photons of light bounce off the ball, travel to my eye, and I can see the ball to measure these things. </li></ul>Wave Behavior of Matter
28. 28. <ul><li>What if I roll an electron down a ramp? </li></ul><ul><li>The photons that hit it move it. </li></ul><ul><li>When the photons reach my eye, the position of the electron has changed. </li></ul><ul><li>I don’t know exactly where the electron is. </li></ul><ul><li>Long story short, I can either know the position or the momentum well, by the equation: </li></ul><ul><li>∆ x * ∆mv ≥h/4 π </li></ul>Wave Behavior of Matter
29. 29. <ul><li>Question: you have to memorize some of the formulas in the chapter, you can either memorize all the one’s you have all ready learned or the next one, you can decide. </li></ul><ul><li>Just think about it and I’ll tell you when you need to decide. </li></ul>Quantum Mechanics & Atomic Orbitals
30. 30. <ul><li>Schrodinger came up with an equation to describe electron (or any particle) waves </li></ul><ul><li>This opened a new way of looking at particles called wave or quantum mechanics </li></ul><ul><li>If you pluck a guitar string a wave travels up and down the string; this is called a standing wave </li></ul><ul><li>Schrodinger came up with an equation to describe a function to describe the electron’s probable position on an allowed energy state </li></ul><ul><li>(Ok, now you have to decide on the equations) </li></ul>Quantum Mechanics & Atomic Orbitals
31. 31. <ul><li>The Schrodinger wave equation describes the probability of an electron’s position when in a given allowed energy state. </li></ul>Quantum Mechanics & Atomic Orbitals
32. 32. <ul><li>Solving the wave equation gives a list of densities where an electron can be found when in a particular energy state. </li></ul><ul><li>The densities associated with an energy is called an orbital (orbital ≠ orbit) </li></ul><ul><li>The Bohr model used one quantum number (n) to describe the energy state, quantum mechanics uses three, n, l, and m </li></ul>Quantum Mechanics & Atomic Orbitals
33. 33. Quantum Mechanics & Atomic Orbitals <ul><li>The principal quantum number (n) can have positive integer values. The bigger n is, the higher the energy of the electron </li></ul><ul><li>The second number (l) is the angular momentum number. </li></ul><ul><ul><li>It can have values from 0 to (n-1). </li></ul></ul><ul><ul><li>Each number has a differently shaped orbital </li></ul></ul><ul><ul><li>Each number (l) for a given orbital (n) is designated by a letter </li></ul></ul>f d p s Letter 3 2 1 0 l=
34. 34. Quantum Mechanics & Atomic Orbitals <ul><li>m is the magnetic quantum number. m can have integer values from –l to l </li></ul>
35. 35. <ul><li>Each principal quantum number, n, is called the shell </li></ul><ul><li>Each shell has sub-shells. The number of sub-shells equals the shell number. The sub-shells correspond to l </li></ul><ul><li>Each sub-shell has orbitals equal to m (that makes 2l+1 orbitals) </li></ul>Quantum Mechanics & Atomic Orbitals
36. 36. Quantum Mechanics & Atomic Orbitals 16 7 -3,-2,-1, 0,1,2,3 4f 3     5 -2,-1,0,1,2 4d 2     3 -1,0,1 4p 1     1 0 4s 0 4 9 5 -2,-1,0,1,2 3d 2     3 -1,0,1 3p 1     1 0 3s 0 3 4 3 -1,0,1 2p 1     1 0 2s 0 2 1 1 0 1s 0 1 Total orbitals in the shell Orbitals in sub shell Possible values of m Sub shell designation Possible values of l n (shell)
37. 37. <ul><li>The s orbitals </li></ul><ul><li>The wave function yields a shape that is like a hollow sphere centered at the nucleus </li></ul><ul><li>It’s not an “M&M” shell, more like a fuzzy tennis ball </li></ul><ul><li>As n increases, the shell expands, kind of </li></ul><ul><li>The wave equation indicates areas of probability outside of the “ball’s surface” </li></ul>Representing Orbitals
38. 38. Representing Orbitals
39. 39. <ul><li>p orbitals </li></ul><ul><ul><li>They have two teardrop lobes </li></ul></ul><ul><ul><li>The lobes DO NOT TOUCH </li></ul></ul><ul><ul><li>The three orbitals are arranged on the three axis and called p x , p y , and p z </li></ul></ul>Representing Orbitals
40. 40. Representing Orbitals Actual probability distribution for a p orbital. Notice there are no dots at x=y=z=0
41. 41. <ul><li>d and f orbitals </li></ul><ul><ul><li>When n=> 3, d orbitals are formed </li></ul></ul><ul><ul><li>There are five of them </li></ul></ul><ul><ul><li>Four look like 4 – leaf clovers, the other like a p orbital with a belt. </li></ul></ul>Representing Orbitals
42. 42. Representing Orbitals
43. 43. <ul><li>f orbitals occur when n=>4 </li></ul><ul><li>There are 7 of them </li></ul><ul><li>Just know that there are there </li></ul>Representing Orbitals
44. 44. Representing Orbitals
45. 45. <ul><li>Unlike the Hydrogen atom, other atoms have more then one electron. </li></ul><ul><li>When you look at the spectral lines from these atoms, there are actually TWO closely spaced lines. </li></ul><ul><li>It was postulated that each orbital had TWO electrons. </li></ul><ul><li>So a new quantum number, the spin magnetic number (m s ) was created </li></ul><ul><li>m s can have a value of +1/2 or -1/2 </li></ul>Electron Spin
46. 46. <ul><li>Pauli exclusion principle – no two electrons in an atom can have set of four quantum numbers. </li></ul><ul><li>That means each orbital can have 2 electrons in it. </li></ul><ul><li>Lithium (Li) has three electrons: </li></ul><ul><ul><li>Li  n1, s, m s 1/2 </li></ul></ul><ul><ul><ul><li> n1, s, m s -1/2 </li></ul></ul></ul><ul><ul><ul><li> n2, s, m s ½ </li></ul></ul></ul><ul><li>Orbitals are filled from LOWEST to HIGHEST as we will see next </li></ul>Electron Spin
47. 47. <ul><li>How do we diagram the electron configuration? </li></ul><ul><li>Each orbital in an atom is represented by a box. </li></ul><ul><li>The boxes are arranged in order of increasing energy </li></ul><ul><li>Each box can have 2 arrows ( ↑↓), one for each magnetic spin number </li></ul>Electron Configuration
48. 48. Electron Configuration
49. 49. <ul><li>s orbitals take both electrons before the p orbital starts filling </li></ul><ul><li>Higher orbitals like p and d fill up one electron at a time – i.e. one electron in each orbital until they all have one, then back to the beginning the second electron. </li></ul>Electron Configuration
50. 50. Electron Configuration
51. 51. <ul><li>Condensed notation </li></ul><ul><li>By the time you get to the third period, there’s a lot of orbitals to write. </li></ul><ul><li>To save time, we write the noble gas from the last period, then start with the new shell. </li></ul><ul><li>Remember that the noble gas from the period above has all the orbitals up to tht point full. </li></ul>Electron Configuration
52. 52. Electron Configuration Each [Ne] represents the shells 1s 2 2s 2 2px 2 2py 2 2pz 2 . It’s a lot easier to write [Ne]
53. 53. <ul><li>Transition metals fourth period </li></ul><ul><ul><li>Both s orbitals get filled first </li></ul></ul><ul><ul><li>Next the period THREE d orbitals get filled </li></ul></ul><ul><ul><li>Then the period 4 p orbitals get filled </li></ul></ul><ul><li>Series metals (period 6) </li></ul><ul><ul><li>Both 6s orbitals get filled first </li></ul></ul><ul><ul><li>Next one 5d orbital get filled </li></ul></ul><ul><ul><li>Then the 4f orbitals get filled </li></ul></ul><ul><ul><li>Then back to the 5d orbitals </li></ul></ul><ul><ul><li>Then pack to the 6p orbitals </li></ul></ul><ul><li>This is confusing and you will never use this again unless you study chemistry. </li></ul>Electron Configuration
54. 54. Electron Configuration & the Periodic Table
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