Atomic Structure

1. AP Notes Chapter 6 • Describe properties of electromagnetic radiation • Light & relationship to atomic structure • Wave-particle duality • Basic ideas of quantum mechanics • Quantum numbers & atomic structure Atomic Structure

2. Electromagnetic Spectrum

3. Light • Made up of electromagnetic radiation. • Waves of electric and magnetic fields at right angles to each other. Parts of a wave Wavelength l Frequency (n) = number of cycles in one second Measured in hertz 1 hertz (hz) = 1 cycle/second

4. EMR - Wave Nature c =  where c = Speed of light  = wavelength  = frequency

5. 

6. EMR - Particle Nature(Quantized) Planck: E = hE = energyh = Planck’s constant = 6.626 x 10- 34 J. s= frequency

7. Reminder

8. Kinds of EM waves • There are many different l and n • Radio waves, microwaves, x rays and gamma rays are all examples. • Light is only the part our eyes can detect. G a m m a R a d i o w a v e s R a y s

9. The speed of light • in a vacuum is 2.998 x 108 m/s • = c • c = ln = wavelength x frequency • What is the wavelength of light with a frequency 5.89 x 105 Hz? • What is the frequency of blue light with a wavelength of 484 nm?

10. In 1900(s) • Matter and energy were seen as different from each other in fundamental ways. • Matter was particles. • Energy could come in waves, with any frequency. • Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.

11. Energy is Quantized • Planck found DE came in chunks with size hn • DE = nhn or nhc/l • where n is an integer. • and h is Planck’s constant • h = 6.626 x 10-34 J s • these packets of hn are called quantum

12. Einstein is next • Said electromagnetic radiation is quantized in particles called photons. • Each photon has energy = hn = hc/l • Combine this with Einstein’s E = mc2 • You get the apparent mass of a photon. • m = h / (lc)

13. Neils Bohr (1885 –1962) Bohr Model of the Hydrogen Atom

14. Bohr model of the atom In the Bohr model, electrons can only exist at specific energy levels (orbit). Energy

15. The Bohr Ring Atom n = 4 n = 3 n = 2 n = 1

17. Bohr Model of AtomPostulates P1: e- revolves around the nucleus in a circular orbit

18. Bohr Model of AtomPostulates P2: Only orbits allowed are those with angular momentum of integral multiples of:

19. Bohr Model of AtomPostulates P3: e- does not radiate energy in orbit, but gains energy to go to higher levelallowed orbit & radiatesenergy when falling to lower orbit

20. Photo Absorption and Emission

21. The Bohr Model • n is the energy level • for each energy level the energy is • Z is the nuclear charge, which is +1 for hydrogen. • E = -2.178 x 10-18J (Z2 / n2 ) • n = 1 is called the ground state • when the electron is removed, n = ¥ • E = 0

22. We are worried about the change • When the electron moves from one energy level to another. • DE = Efinal - Einitial • DE = -2.178 x 10-18J Z2 (1/ nf2 - 1/ ni2)

23. Rotating Object Balance • Centrifugal Force= electrical attraction of positive nucleus and negative e-

24. Centrifugal Force = Electrostatic Attraction

25. Definition • Angular Momentum = mvr • By P2:

26. By rearrangement:

27. By rearrangement:

30. For H-atom [n = 1]r = 5.29 x 10 -11 mor52.9 pm = 0.529 Angstoms

31. In general, when n = orbit a0 = radius of H-atom for n = 1 & Z = atomic #

32. To keep e- in orbit, must balance kinetic energy and potential energy

34. where k = Rydberg constant k = 2.179 x 10-18 J

35. For the transition of an e- from an initial energy level (Ei) to a final energy level (Ef), we can write

38. Examples • Calculate the energy need to move an electron from its to the third energy level. • Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. • Calculate the energy released when an electron moves from n= 5 to n=3 in a He+1 ion

39. When is it true? • Only for hydrogen atoms and other monoelectronic species. • Why the negative sign? • To increase the energy of the electron you make it closer to the nucleus. • the maximum energy an electron can have is zero, at an infinite distance.

40. The Bohr Model • Doesn’t work. • Only works for hydrogen atoms. • Electrons don’t move in circles. • The quantization of energy is right, but not because they are circling like planets.

41. Which is it? • Is energy a wave like light, or a particle? • Yes • Concept is called the Wave-Particle duality. • What about the other way, is matter a wave? • Yes

42. The Quantum Mechanical Model • A totally new approach. • De Broglie said matter could be like a wave. • De Broglie said they were like standing waves. • The vibrations of a stringed instrument.

43. Matter as a wave • Using the velocity v instead of the wavelength n we get. • De Broglie’s equation l = h/mv • Can calculate the wavelength of an object.

44. Examples • The laser light of a CD is 7.80 x 102 m. What is the frequency of this light? • What is the energy of a photon of this light? • What is the apparent mass of a photon of this light? • What is the energy of a mole of these photons?

45. What is the wavelength? • Of an electron with a mass of 9.11 x 10-31kg traveling at 1.0 x 107m/s? • Of a softball with a mass of 0.10 kg moving at 125 mi/hr?

46. Diffraction • Diffraction Grating splits light into its components of light of different frequencies or wavelengths. • When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effect • Because the waves interfere with each other.

47. A wave moves toward a slit.

48. Comes out as a curve

49. with two holes

50. Two Curves with two holes