LIGHT and Planck's Constant

1. LIGHT and Planck's Constant DO NOW: Using your textbooks answer the following What is mass spectrometry and how is it used? Define light What is the formula for Planck’s constant and what does each variable represent

2. The study of light led to the development of the quantum mechanical model. • Light is a kind of electromagnetic radiation. (radiant energy) • Electromagnetic radiation includes many kinds of waves • All move at 3.00 x 108 m/s ( c) Light

3. Crest Wavelength Amplitude Trough Orgin Parts of a wave

4. Orgin - the base line of the energy. • Crest - high point on a wave • Trough - Low point on a wave • Amplitude - distance from origin to crest • Wavelength - distance from crest to crest • Wavelength - is abbreviated l Greek letter lambda. Parts of Wave

5. Waves • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength().

6. Waves • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

7. Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. • Therefore, c = 

8. The number of waves that pass a given point per second. • Units are cycles/sec or hertz (hz) • Abbreviated n the Greek letter nu c = ln Frequency

9. Are inversely related • As one goes up the other goes down. • Different frequencies of light is different colors of light. • There is a wide variety of frequencies • The whole range is called a spectrum Frequency and wavelength

10. High energy Low energy Low Frequency High Frequency X-Rays Radiowaves Microwaves Ultra-violet GammaRays Infrared . Long Wavelength Short Wavelength Visible Light

11. Energy is quantized. • Light is energy • Light must be quantized • These smallest pieces of light are called photons. • Energy and frequency are directly related. Light is a Particle

12. E = h x n • E is the energy of the photon • n is the frequency • h is Planck’s constant • h = 6.6262 x 10 -34 Joules sec. • joule is the metric unit of Energy Energy and frequency

13. The Nature of Energy • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.

14. The Math • Only 2 equations • c = λν • E = hν • Plug and chug.

15. The Nature of Energy • Einstein used this assumption to explain the photoelectric effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63  10−34 J-s.

16. The Nature of Energy • Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

17. What is the wavelength of blue light with a frequency of 8.3 x 1015hz? • What is the frequency of red light with a wavelength of 4.2 x 10-5 m? • What is the energy of a photon of each of the above? Examples

18. HW 6.11, 6.12, 6.14, 6.17, 6.18

19. The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

20. The Nature of Energy • One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.

21. Waves • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength().

22. Waves • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

23. Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. • Therefore, c = 

24. The Nature of Energy • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.

25. The Nature of Energy • Einstein used this assumption to explain the photoelectric effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63  10−34 J-s.

26. The Nature of Energy • Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

27. The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

28. The Nature of Energy • One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.

29. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

30. Atomic Spectrum How color tells us about atoms

31. Atomic Spectrum How color tells us about atoms

32. Prism • White light is made up of all the colors of the visible spectrum. • Passing it through a prism separates it.

33. If the light is not white • By heating a gas with electricity we can get it to give off colors. • Passing this light through a prism does something different.

34. Atomic Spectrum • Each element gives off its own characteristic colors. • Can be used to identify the atom. • How we know what stars are made of.

35. These are called discontinuous spectra • Or line spectra • unique to each element. • These are emission spectra • The light is emitted given off.

36. The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

37. The Nature of Energy • One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.

38. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

39. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

40. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h

41. 1 nf2 ( ) - E = −RH 1 ni2 The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron.

42. h mv  = • Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass and wavelength was The Wave Nature of Matter

43. h 4 (x) (mv)  • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! The Uncertainty Principle

44. Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics.

45. Quantum Mechanics • The wave equation is designated with a lower case Greek psi (). • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

46. Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. Quantum Numbers

47. The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 0. Principal Quantum Number, n

48. This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. Azimuthal Quantum Number, l

49. Azimuthal Quantum Number, l

50. Describes the three-dimensional orientation of the orbital. • Values are integers ranging from -l to l: −l ≤ ml≤ l. • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. Magnetic Quantum Number, ml