1. 1 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Section 7 Quantum Theory of the Atom

2. 2 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Wave Nature of Light A wave is a continuously repeating change or oscillation in matter or in a physical field. Light is also a wave. –It consists of oscillations in electric and magnetic fields that travel through space. –Visible light, X rays, and radio waves are all forms of electromagnetic radiation.

3. 3 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Wave Nature of Light A wave can be characterized by its wavelength and frequency. –The wavelength,  (lambda), is the distance (m or nm) between any two adjacent identical points of a wave. –The frequency,  (nu), of a wave is the number of wavelengths that pass a fixed point in one second (1/s or s -1 or Hz).

4. 4 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –So, given the frequency of light, its wavelength can be calculated, or vice versa. The Wave Nature of Light The product of the frequency, (waves/sec) and the wavelength, (m/wave) would give the speed of the wave in m/s (note: freq and wavelength are inversely proportional). –In a vacuum, the speed of light, c, is 3.00 x 10 8 m/s. Therefore,

5. 5 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Wave Nature of Light What is the wavelength of yellow light with a frequency of 5.09 x 10 14 s -1 ? (Note: s -1, commonly referred to as Hertz (Hz) is defined as “cycles or waves per second”.)

6. 6 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. What is the frequency of violet light with a wavelength of 408 nm? The Wave Nature of Light

7. 7 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –Visible light extends from the violet end of the spectrum at about 400 nm to the red end with wavelengths about 800 nm. –Beyond these extremes, electromagnetic radiation is not visible to the human eye. The range of frequencies or wavelengths of electromagnetic radiation is called the electromagnetic spectrum. High E and v, small Low E and v, large HW 57

8. 8 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Effects and Photons By the early part of twentieth century, the wave theory of light seemed to be well entrenched. –In 1905, Albert Einstein proposed that light had both wave and particle properties as observed in the photoelectric effect. –Einstein based this idea on the work of a German physicist, Max Planck, in 1900.

9. 9 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Effects and Photons Planck’s Quantization of Energy (1900) –According to Max Planck, the atoms of a solid oscillate with a definite frequency,. where h (Planck’s constant) is assigned a value of 6.626 x 10 -34 J. s and n must be an integer. –He proposed that an atom could have only certain energies of vibration, E, those allowed by the formula

10. 10 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Effects and Photons Planck’s Quantization of Energy. –Thus, the only energies a vibrating atom can have are 1h, 2h, 3h, and so forth. –The numbers symbolized by n are one of the four quantum numbers we will discuss later. –The vibrational energies of the atoms are said to be quantized.

11. 11 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Effects and Photons Photoelectric Effect –Einstein extended Planck’s work to include the structure of light itself. If a vibrating atom changed energy from 3h (higher level) to 2h (lower level), it would decrease in energy by h (photon). He proposed that this energy would be emitted as a bit (or quantum) of light energy. Einstein postulated that light consists of quanta (now called photons), or particles of electromagnetic energy.

12. 12 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Effects and Photons Photoelectric Effect –The energy of the photons proposed by Einstein would be proportional to the observed frequency, and the proportionality constant would be Planck’s constant. –In 1905, Einstein used this concept to explain the “photoelectric effect.”

13. 13 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –The photoelectric effect is the ejection of electrons from the surface of a metal when light shines on it. Quantum Effects and Photons Photoelectric Effect –Electrons are ejected only if the light is a certain “threshold” frequency of the particular metal. –Violet light, for example, will cause potassium to eject electrons, but no amount of red light (which has a lower frequency) has any effect.

14. 14 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –Einstein’s assumption that an electron is ejected when struck by a single photon implies that light behaves like a particle. Quantum Effects and Photons Photoelectric Effect –When the photon hits the metal, its energy, h is taken up by the electron. –The photon ceases to exist as a particle; it is said to be “absorbed.”

15. 15 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –Wave-Particle Duality of light - the “wave” and “particle” pictures of light should be regarded as complementary views of the same physical entity. Quantum Effects and Photons Photoelectric Effect The equation E = h displays this duality; E is the energy of the “particle” photon, and is the frequency of the associated “wave.”

16. 16 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Radio Wave Energy What is the energy of a photon corresponding to radio waves of frequency 1.255 x 10 6 Hz? HW 58

17. 17 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Atomic Line Spectra –When a heated metal filament emits light, we can use a prism to spread out the light to give a continuous spectrum-that is, a spectrum containing light of all wavelengths. –The light emitted by a heated gas, such as hydrogen, results in a line spectrum-a spectrum showing only specific wavelengths of light. The Bohr Theory of the Hydrogen Atom

18. 18 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure: Emission (line) spectra of some elements.

19. 19 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Atomic Line Spectra –In 1885, J. J. Balmer showed that the wavelengths,, in the visible spectrum of hydrogen could be reproduced by a simple formula. –The known wavelengths of the four visible lines for hydrogen correspond to values of n = 3, n = 4, n = 5, and n = 6 (electrons jump down from higher level to second level). The Bohr Theory of the Hydrogen Atom

20. 20 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure : Transitions of the electron in the hydrogen atom.

21. 21 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Bohr Theory of the Hydrogen Atom Prior to the work of Niels Bohr, the stability of the atom could not be explained using the then-current theories. –In 1913, using the work of Einstein and Planck, Bohr applied a new theory to the simplest atom, hydrogen.

22. 22 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Bohr’s Postulates –Bohr set down postulates to account for (1) the stability of the hydrogen atom and (2) the line spectrum of the atom. 1. Energy level postulate An electron can have only specific energy levels in an atom. 2. Transitions between energy levels An electron in an atom can change energy levels by undergoing a “transition” from one energy level to another. 3. Angular momentum keeps electrons in orbit. The Bohr Theory of the Hydrogen Atom

23. 23 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Bohr’s Postulates –Bohr derived the following formula for the energy levels of the electron in the hydrogen atom. –R h is a constant (expressed in energy units) with a value of 2.18 x 10 -18 J. The Bohr Theory of the Hydrogen Atom

24. 24 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Bohr’s Postulates –When an electron undergoes a transition from a higher energy level to a lower one, the energy is emitted as a photon. –From Postulate 1, The Bohr Theory of the Hydrogen Atom

25. 25 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Bohr’s Postulates –If we make a substitution into the previous equation that states the energy of the emitted photon, h, equals E i - E f, Rearranging, we obtain The Bohr Theory of the Hydrogen Atom Energy of photon

26. 26 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Bohr’s Postulates –Bohr’s theory explains not only the emission of light, but also the absorption of light. –When an electron falls from n = 3 to n = 2 energy level, a photon of red light (wavelength, 685 nm) is emitted. –When red light of this same wavelength shines on a hydrogen atom in the n = 2 level, the energy is gained by the electron that undergoes a transition to n = 3. The Bohr Theory of the Hydrogen Atom

27. 27 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider Calculate the energy of a photon of light emitted from a hydrogen atom when an electron falls from level n = 3 to level n = 1. HW 59

28. 28 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.

29. 29 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Mechanics Bohr’s theory established the concept of atomic energy levels but did not thoroughly explain the “wave-like” behavior of the electron. –Current ideas about atomic structure depend on the principles of quantum mechanics, a theory that applies to subatomic particles such as electrons.

30. 30 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The first clue in the development of quantum theory came with the discovery of the de Broglie relation. –In 1923, Louis de Broglie reasoned that if light exhibits particle aspects, perhaps particles of matter show characteristics of waves. –He postulated that a particle with mass m and a velocity v has an associated wavelength. –The equation  = h/mv is called the de Broglie relation. Quantum Mechanics

31. 31 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. If matter has wave properties, why are they not commonly observed? –Does a baseball (0.145 kg) moving at about 60 mph (27 m/s) have a wavelength? Yes, about 1.7 x 10 -34 m. –This value is so incredibly small that such waves cannot be detected. Quantum Mechanics

32. 32 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Mechanics Quantum mechanics is the branch of physics that mathematically describes the wave properties of submicroscopic particles. –We can no longer think of an electron as having a precise orbit (spherical) in an atom. –To describe such an orbit would require knowing its exact position and velocity. –In 1927, Werner Heisenberg showed (from quantum mechanics) that it is impossible to know both (position & velocity) simultaneously – Heisenberg’s Uncertainty Principle.

33. 33 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Mechanics Although we cannot precisely define an electron’s orbit, we can obtain the highest probability of finding an electron at a given point around the nucleus.

34. 34 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Numbers and Atomic Orbitals According to quantum mechanics, each electron is described by four quantum numbers. –The first three define the wave function for a particular electron. The fourth quantum number refers to the magnetic property of electrons. – – Principal quantum number (n) –Angular momentum quantum number (l) –Magnetic quantum number (m l ) –Spin quantum number (m s )

35. 35 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –The smaller n is, the smaller the orbital. –The smaller n is, the lower the energy of the electron. –May be an integer from 1 to, although greater than 7 as far as today, are unimportant. –n determines the size and energy of the orbital. The effective volume of space electron is moving about. Quantum Numbers and Atomic Orbitals The principal quantum number(n) represents the “shell number or energy level” in which an electron “resides.”

36. 36 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The angular momentum quantum number (l) distinguishes “sub shells” within a given shell that have different shapes (shape of region (volume) that electron occupies). –Each main “shell - n” is subdivided into “sub shells.” Within each shell of quantum number n, there are “l” sub shells, each with a distinctive shape. –l can have any integer value from 0 to (n - 1) –The different subshells are denoted by letters. – Letter s p d f g … – l 0 1 2 3 4 …. Quantum Numbers and Atomic Orbitals

37. 37 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. angular momentum quantum number (l) Quantum Numbers and Atomic Orbitals

38. 38 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure : Cutaway diagrams showing the spherical shape of S orbitals.

39. 39 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure : The 2p orbitals.

40. 40 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure : The five 3d orbitals.

41. 41 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Configurations and the Periodic Table

42. 42 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The magnetic quantum number (m l ) distinguishes orbitals within a given sub-shell that have different shapes and orientations in space (governs the orientation of the orbital). –Each sub shell (s, p, d, f) is subdivided into “orbitals,” each capable of holding a pair of electrons (max 2 electrons/orbital orientation). –m l can have any integer value from -l to 0 to +l. –Each orbital within a given sub shell has the same energy (all “nl” have same energy for all orientations but not each “l” – s<p<d<f). Quantum Numbers and Atomic Orbitals

43. 43 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Figure : The 2p orbitals.

44. 44 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.

45. 45 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The magnetic quantum number (m l ) Quantum Numbers and Atomic Orbitals Hund’s Rule – when orbitals are available in degenerate sets (same energy level) the lowest energy arrangement (the “ground state”) of electrons in a sub-shell is obtained by putting electrons into separate orbitals of the sub shell with the same spin before pairing electrons. Although an electron behaves like a tiny magnet, two electrons that are opposite in spin cancel each other. Only atoms with unpaired electrons exhibit magnetic susceptibility. Paramagnetic substance – is one that weakly attracted by a magnetic field, the result of unpaired electrons. Diamagnetic substance – is not attracted by a magnetic field because it has only paired electrons.

46. 46 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Configurations and the Periodic Table

47. 47 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Electron Configuration An orbital diagram is used to show how the orbitals of a sub shell are occupied by electrons. –Each orbital is represented by a circle or a line. –Each group of orbitals is labeled by its sub shell notation. 1s 2s 2p –Electrons are represented by arrows: up for m s = +1/2 and down for m s = -1/2

48. 48 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Orbital Energy Levels in Multi- electron Systems Energy 1s 2s 2p 3s 3p 4s 3d

49. 49 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The spin quantum number (m s ) refers to the two possible spin orientations of the electrons residing within a given orbital. –Each orbital can hold only two electrons whose spins must oppose one another. –The possible values of m s are +1/2 and –1/2. –Pauli Exclusion Principle – no two electrons may have the same set of 4 quantum numbers. Where two electrons occupy the same orbital, they must have opposite spins: m s +1/2, m s –1/2 Quantum Numbers and Atomic Orbitals

50. 50 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Quantum Numbers and Atomic Orbitals Ex. HW 60