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TOPIC VIII: Electronic Structure in Atoms

TOPIC VIII: Electronic Structure in Atoms. LECTURE SLIDES Electromagnetic Radiation: E, ,  Early Models Quantum Numbers Shells, Subshells, Orbitals. Kotz & Treichel, Chapter 7. WHERE THE ELECTRONS ARE. We are going to examine in historical succession

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TOPIC VIII: Electronic Structure in Atoms

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  1. TOPIC VIII: Electronic Structure in Atoms • LECTURE SLIDES • Electromagnetic Radiation: E, ,  • Early Models • Quantum Numbers • Shells, Subshells, Orbitals Kotz & Treichel, Chapter 7

  2. WHERE THE ELECTRONS ARE..... We are going to examine in historical succession the ideas and experiments that led to the modern atomic theory and sophisticated placement of the electrons about the nucleus. The current theory, based on quantum mechanics, places the electrons around the nucleus of the atom in “ORBITALS,” regions corresponding to allowedenergy states in which an electron has about 90% probability of being found. Let’s see how we got there!

  3. Historical Events, Nature of Electromagnetic Radiation 1. 1864 James Maxwell: Wave motion of electromagnetic radiation 2. 1885 Rydberg, Balmer: Wavelength of atomic spectra 3. 1900 Max Planck: Quantum theory of radiation, packets of specific energy 4. ~1905 Einstein: Particle- like properties of radiation, “photons”

  4. James Maxwell described all forms of radiation in terms of oscillating (wave like) electricand magnetic fields in space. The fields are propagated at right angles to each other. All “forms of radiation” include visible light but also, x-rays, radioactivity, microwaves, radio waves: all are described today as electromagnetic radiation. The waves have characteristic frequency and wavelength, and travel at a constant velocity in a vacuum, 3.0 X 10 8 m/s.

  5. Wave description: Frequency: # cycles / sec

  6. Important Relationship, all electromagnetic radiation: c =  speed light, vacuum = wavelength X frequency 3.00 X 108ms-1=, mX, s-1 (hertz) hertz, Hz, s-1 # cycles per second Same as m/s Rearranging:  = c/  = c/

  7. A red light source exhibits a wavelength of 700 nm, and a blue light source has a wavelength of 400 nm. What is the characteristic frequency of each of these light sources? Red light: 700 nm = ? m =? s-1 700 nm 1m = 700 X 10-9 m = 7.00 X 10-7m 109 nm  = c /  = 3.00 X 108ms-1 = 4.29 X 1014s-1 7.00 X 10-7 m = 4.29 X 1014 cycles per sec = 4.29 X 1014 Hz or s-1

  8. Blue Light: 400 nm = ? m= ? s-1 400 nm 1m = 400 X 10-9 m = 4.00 X 10-7m 109 nm  = c /  = 3.00 X 108ms-1= 7.50 X 10 14s-1 4.00 X 10-7 m = 7.50 X 1014 cycles per sec = 7.50 X 1014 Hz

  9. longer lower RED light: 700 nm, 4.29 X 1014 Hz BLUE light: 400 nm, 7.50 X 1014Hz higher shorter Point to remember:theshorterthe wavelength, the higherthe frequency:the longer the wavelength, the lower the frequency.

  10. GROUP WORK 8.1 Microwave ovens sold in US give off microwave radiation with a frequency of 2.45 GHz. What is the wavelength of this radiation, in m and in nm?  = c/ 2.45 GHz = ? m = ? nm 109 Hz (s-1) = 1 GHz c = 3.00 X 108 ms-1 1. Convert GHz to Hz; call Hz “s-1” 2. Calculate wavelength, , in m 3.Convert m to nm (109 nm = 1 m)

  11. Max Planck made a major step forward with his theory that energy is not continuous but rather is generated in small, measurable packets he called quantum (which refers back to the Latin, meaning bundle). He related the energy of the quantum to its frequency or wavelength as below: For one quantum of radiation: Energy = h x radiation = h x c  radiation h is Planck’s constant, 6.63 X 10-34joulesec

  12. Energy Units The “ calorie”: “The quantity of energy required to raise 1.00 g of water 1oC”. Very small amount of energy, so Kcal are generally used: 1000 calories(cal) = 1 kilocalorie, kcal SI unit of energy is the “joule”, defined in terms of kinetic energy rather than heat energy. One joule is the amount of kinetic energy involved when a 2.0 kg object is moving with a velocity of 1.0 m/s. Again, a very small amount of energy, so kilojoules are generally used: 1000 joules (J) = 1 kilojoule kJ (kJ) Relationship: 1 calorie = 4.184 joules

  13. Sample Calculations: E = h = h c  Blue light,  = 4.00 X 10-7 m E = 6.63 X 10-34 joule s x 3.00 X 108 ms-1 4.00 X 10-7 m E = 4.97 X 10-19 joule Microwave oven,  = 2.45 X 109 Hz or s-1 E = 6.63 X 10-34 joule s x 2.45 X 109 s-1 E = 1.62 X 10-24 joule

  14. The relationships expressed by this equation include the following: Energy of a quantum is directly proportional to the frequency of radiation: high frequency radiation is the highest energy radiation (x rays, gamma rays) Energy of radiation is inversely proportional to its wavelength: long waves are lowest in energy, short waves are highest. Radio waves, microwaves, radar represent low energy forms of radiation. View CD ROM sliding spectra here

  15. Group Work 8.2a: Rank radiation types by increasing energy (#5 = highest) wavelength Energy rank

  16. Group Work 8.2b: Rank radiation types by increasing energy (#5 = highest) frequency Energy rank

  17. Einstein took the next step in line by using Planck’s quantum theory to explain the photoelectric effect in which high frequency radiation can cause electrons to be removed from atoms. Einstein decided that light has not only wave- like properties typical of radiation but also particle- like properties. He renamed Planck’s energy quantum as a “photon”, a massless particle with the quantized energy/frequency relationships described by Planck. “Quantized” refers to properties which have specific allowed values only.

  18. Wavelength, frequency, energy relationships: c, speed of light = Wavelength, Xfrequency,  = c=c  c = 3.00 X 108 ms-1, speed of light in vacuum energy of photon = h, Planck’s constant x  E = h = h c  h = 6.63 X 10-34 joule s

  19. It was discovered in this time frame that each element which was subjected to high voltage energy source in the gas state would emit light. When this light is passed through a prism, instead of obtaining a continuous spectrum as one obtains for white light, one observes only a few distinct lines of very specific wavelength. Each element emits when “excited” its own distinct “line emission spectrum” with identifying wavelengths. This important discovery lead directly to our modern understanding of electronic structure in the atom! Checkout CD-ROM...

  20. Historical Events, the Nature of Electron 1. 1804 Dalton: Indivisible atom 2. 1897 Thomson: Discovery of electrons 3. 1904 Thomson: Plum Pudding atom 4. 1909 Rutherford: The Nuclear atom 5. 1913 Bohr: Planetary atom model, e’s in orbits

  21. JJ Thompson’s Picture of the atom:

  22. Rutherford’s Picture of the Atom:

  23. Bohr combined the ideas we have met to present his “planetary” model of the atom, with the electrons circling the nucleus like planets around the sun:

  24. Bohr used all the ideas to date: • electron in the atom outside the tiny positive nucleus • excited elements emit specific wavelengths of energy • only • radiation comes in packets of specific energy and • wavelength Bohr’s atom placed the electrons in energy quantized orbits about the nucleus and calculated exactly the energy of the electron for hydrogen in each orbit.

  25. Bohr also predicted that each shell or orbit about the nucleus would have its occupancy limited to 2n2electrons, where n = the orbit number. Many of Bohr’s ideas, in modified form, remain in the present day quantum mechanics description of atomic structure. Bohr was able to calculate exactly the energy values for the hydrogen spectrum using his model; however the calculations only worked for one electron systems and did not explain the electronic behavior of larger atoms.

  26. GROUP WORK 8.3 Predict maximum occupancy (2n2 )of each shell: n=1 = _____ e’s n=5 = _____ e’s n=2 = _____ e’s n=6 = _____ e’s n=3 = _____ e’s n=7= _____ e’s n=4 = _____ e’s

  27. Summation: Planck Energy is “quantized”, comes in packets called quantum with energy hv Einstein Energy can interact with matter, photoelectric effect, quantum renamed “photon” Bohr Photons of energy can interact with electrons in orbits of lowest possible energy around the nucleus and “excite” e’s to higher energy orbits. The e’s give off this energy as light, spectral lines as they return to “ground” state.

  28. Electron as matter/energy particle 1. 1925 DeBroglie: Matter Waves 2. 1926 Heisenberg’s Uncertainty Principle 3. 1926 Schroedinger’s Wave Equation and Wave Mechanics 4. Modern Theory: Use of wave equation to describe electron energy/probable location in terms of three quantum numbers.

  29. DeBroglie next suggested that all matter moved in wavelike fashion, just like radiation. Large macroscopic matter (moving golf balls, raindrops, etc) have characteristic wavelengths associated with their motion but the wavelengths are too tiny to be detectable or significant. Electrons, on the other hand have very significantwavelengths in comparison to their size. Einstein gave radiation matter- like, particle properties; DeBroglie gave matter wave- like properties.

  30. Heisenberg’s Uncertainty Principle: If an electron has some properties that are wave like and others that are like particles, we cannot simultaneously describe the exact location of the electron and its exact energy. The accurate determination of one changes the value of the other. The Bohr atom tried to describe exact energy and position for the e’s around the nucleus and worked only for H.

  31. Born’s interpretation of Heisenberg’s Uncertainty Principle: If we want to make an accurate statement about the energy of an electron in the atom, we must accept some uncertainty in its exact position. We can only calculate probable locations where an electrons is to be found. Schroedinger’s wave equation describes the electron as as a moving matter wave, and results in a picture in which we place electrons in probable locations about the nucleus based on their energy.

  32. Schroedinger’s Wave Equation The mathematics employed by Schroedinger to describe the energy and probable location of the electron about the nucleus is complex and only recently been solved for larger atoms than hydrogen. However, it yields a description of the atom which accounts for the differences between the elements. IT WORKS!

  33. Schroedinger’s wave equation describes the electrons in a given atom in terms of probable regions of differing energies in which an electron is most likely to be found. We call the regions “orbitals” rather than “orbits”, and each is centered about the nucleus. The description of each orbital is given in the form of three “quantum numbers”, which give an address - like assignment to each orbital. The quantum numbers are in the form of a series of solutions to the wave equation.

  34. Summation: Heisenberg: Uncertainty Principle: cannot determine simultaneously the exact location and energy of an electron in atom Schroedinger: Wave equation to calculate probable location of e’s around nucleus using dual matter/wave properties of e’s. Three quantum numbers from equation locate e’s of various energies in probable main shells, subshells, orbitals.

  35. Group Work 8.4: MatchScientist with Contribution

  36. QUANTUM NUMBERS The Quantum Numbers “Locators, which describe each e- about the nucleus in terms of relative energy and probable location.” The first quantum number, n, locates each electron in a specific main shell about the nucleus. The secondquantum number, l , locates the electron in a subshell within the main shell. The third quantum number, ml, locates the electron in a specific orbitalwithin the subshell.

  37. Locator #1, “n”, the first quantum number • “n”, the Principal quantum number: • Has all integer values 1 to infinity: 1,2,3,4,... • Locates the electron in an orbital in a main shell • about the nucleus, like Bohr’s orbits • describes maximum occupancy of shell, 2n2. • The higher the n number: • the larger the shell • the farther from the nucleus • the higher the energy of the orbital in the shell.

  38. Locator #2, “l”, the second quantum number • locates electrons in a subshellregion within the • main shell • limits number of subshells per shell to a value equal to n: • n =1, 1 subshell • n = 2, 2 subshells • n= 3, 3 subshells ..... • only four types of subshells are found to be • occupied in unexcited, “ground state” of atom. • These subshell types are known by letter: • “s” “p” “d ” “f”

  39. Diagram of available shells and subshells On the next slide is a schematic representation of the shells and subshells available for electron placement within the atom. Note that the 5th, 6th and 7th types are given the alphabetical letters following “f”. None of these types are occupied in the ground state of the largest known atoms.

  40. n = 7 7s (7p 7d 7f 7g 7h 7i) Highest, biggest n = 6 6s 6p 6d (6f 6g 6h) n = 5 5s 5p 5d 5f (5g) n = 4 4s 4p 4d 4f n = 3 3s 3p 3d n = 2 2s 2p 1s n = 1 Lowest energy, smallest shell

  41. Locator #3, “ml”,the third quantum number “ml”, the third quantum number, specifies in which orbitalwithin a subshell an electron may be found. It turns out that each subshell type contains a unique number of orbitals, all of the same shape and energy. Main shell subshells orbitals ml # n# l #

  42. The Third Q#, ml continued “ml” values will describe the number of orbitals within a subshell, and give each orbital its own unique “address”: s subshell p subshell dsubshellf subshell 1 orbital 3 orbitals 5 orbitals 7 orbitals

  43. “l” “ml” f f f f f f f f d d d d d d p p p p s s

  44. All electrons can be located in an orbital within a subshellwithin a main shell. To find that electron one need a locating value for each: the “n” number describes a shell (1,2,3...) the “l” number describes a subshell region (s,p,d,f...) the “ml” number describes an orbital within the region (Each of these quantum numbers has a series of numerical values. We will only use the n numerical values, 1-7.)

  45. Group Work 8.5

  46. The 4th Quantum Number, ms It was subsequently discovered that each orbital we have described is home to not just one but two electrons, with opposite spins! We are now treating an electron as a spinning charged matter particle, rotating clockwise or counterclockwise on its axis: (next slide) To describe this situation, a fourth quantum number is required, the magnetic quantum number, “ms”.

  47. As a consequence, we now know: ssubshell, one orbital,2 e’s psubshell, three orbitals,6 e’s, d subshell, five orbitals, 10 e’s, f subshell, seven orbitals, 14e’s,

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