The Chemical Part of the Atom

1. The Chemical Part of the Atom Electronic Structure of Atoms

2. Electromagnetic Spectrum

3. Electromagnetic Spectrum The electromagnetic spectrum is a continuum of all electromagnetic waves arranged according to frequency and wavelength. Electromagnetic energy passes through space at the speed of light in the form of sinusoidal waves.

4. Electromagnetic Wave

5. Sinusoidal Wave Any oscillation, such as a sound wave or alternating current, whose waveform is that of a sine curve

6. Visible Spectrum The part of the electromagnetic spectrum visible to the human eye, extending from extreme red, 760.6 nanometers, to extreme violet, 393.4 nanometers.

7. Visible Spectrum

8. Radiations The radiations of the electromagnetic (EM) spectrum vary in wavelength, frequency, and energy. What is the relationship: • between wavelength and frequency? - between frequency and energy? - between wavelength and energy?

9. Wavelength, Frequency, & Energy

10. Wave Characteristics Waves have several characteristics; wavelength, frequency, amplitude, energy, velocity

11. Radiations travel as a series of crests and troughs

12. Wavelength is defined as the distance between identical points on successive waves measured in length units; m, cm, nm, Ǻ ( 1 Ǻ = 10-10 m) symbol for wavelength is lambda, λ

13. Frequency is defined as the number of wavelengths produced in a given time period It is often defined as the number of waves (cycles) passing a given point in one second Units of frequency are waves (cycles)/sec; /s; s -1; Hz • 1 Hz = 1 wave(cycle)/sec = /s Symbol for frequency is nu, ν [In newer texts , f may be used]

14. Amplitude is the maximum displacement from the norm • “Height of the wave” The energy carried by a normal wave such as water is related to the wave’s amplitude • How is the energy of a wave imparted? • This will be different for electromagnetic radiation!

15. Amplitude

16. Wave Velocity The speed (velocity) at which a wave travels is equal to the product of its wavelength and frequency v = λν All electromagnetic radiation travels at the same speed, the speed of light The symbol for the speed of light is c c = 3.00 x 108 m/s Therefore, by substitution, the equation becomes c = λν for electromagnetic radiation

17. Max Planck Studied the emissions of metals heated to various temperatures One of his conclusions is: energy is not a smooth flowing continuum, but rather, it is manifested by the emission from radiating bodies of discrete particles called quanta. This becomes the basis for what is known as the quantum theory Light is quantized; given particle character

18. Planck cont’d • Planck is able to establish the relationship between the energy radiated and the frequency of the emissions • As a result the energy of a quantum of radiation may be determined if its frequency is known • Ephoton = h ν • Planck’s constant, h = 6.6262 x 10-34 J-s or 6.6262 x 10-34 J/Hz (these are identical)

19. Photoelectric Effect

20. Photoelectric Effect • Predictions of the wave theory of light: • 1.Light of any frequency will cause electrons to be emitted. • 2.The more intense the light the more kinetic energy the emitted electrons will have. • What actually happens: • 1. Light below a certain cutoff frequency, no matter how intense, will not cause any electrons to be emitted. • 2. Light above the cutoff frequency, even if it's not very intense, will always cause electrons to be emitted. • Above the cutoff frequency, turning up the intensity produces more electrons but does not change the maximum kinetic energy of the electrons.

21. Photoelectric Effect • The explanation in terms of light being made up of photons: • - To eject one electron from the metal takes one photon. • - Electrons are bound to the metal by a binding energy we call the work function, Wo, which differs from metal to metal. If the photon energy is less than the work function, no electrons are emitted. • - The cutoff frequency fo is where the photon energy hfo = Wo • - Above the cutoff frequency the photons have more energy than what is needed to eject an electron. The extra energy shows up as the electron's kinetic energy: K.E.max = E - Wo = hf - Wo

22. Neils Bohr • Electrons traveled in fixed circular pathways about the nucleus called orbits • Each orbit was located at a specific distance from the nucleus • Each orbit represented a specific amount of energy • The further the orbit was from the nucleus, the more energy was associated with it

23. Bohr Atom • Electrons traveling in an orbit possessed and maintained the energy of that orbit • Therefore, the electrons didn’t radiate any energy from these orbits • This implied that atoms and their electrons weren’t governed by the classical laws of mechanics • Electrons may transition between different orbits by gaining or losing energy

24. Bohr Atom • Bohr believed that each orbit had a maximum number of electrons that it could hold • Therefore, no electron was permitted to shift into a “full” orbit • Bohr believed that the electrons of an atom would naturally occupy positions of least energy • Why? • This is referred to as the ground state of the atom • The orbit of least energy was that closest to the nucleus and that of greatest energy was furthest from the nucleus • Any time the atom was exposed to external energy, some of which was absorbed by its electrons, the atom would enter an excited state

25. Energy of a Bohr orbit • E proportional to 1/n2 • E = - RH (1/n2) RH is the Rydberg constant and has the value 2.179 x 10-18 J • The negative sign represents a more stable state with respect to some value or reference • the more negative the value, the more stable the state • The reference state for hydrogen is the complete ionization of the atom (N = ∞) • E = - RH / ∞2 is driven to equal 0

26. Bohr atom cont’d • Recognize that as n increases, the energy difference between the shells decreases

27. Bohr atom cont’d • The lowest energy or most stable state, with n = 1 is called the ground state • Any time the electrons do not represent a ground state condition, the atom is said to be in an excited state • This results when one or more electrons absorb energy and shift to an energy level (shell) of greater energy or orbital diameter

28. Spectra

29. Emission or bright-line spectra • Thus, emission spectra are produced by thin gases in which the atoms do not experience many collisions (because of the low density). The emission lines correspond to photons of discrete energies that are emitted when excited atomic states in the gas make transitions back to lower-lying levels.

30. Continuous spectrum • A continuum spectrum results when the gas pressures are higher, so that lines are broadened by collisions between the atoms until they are smeared into a continuum. We may view a continuous spectrum as an emission spectrum in which the lines overlap with each other and can no longer be distinguished as individual emission lines.

31. Absorption spectrum • An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the same direction as the absorbed photon, this gives rise to dark lines (absence of light) in the spectrum

32. Hydrogen’s spectra

33. Spectra of Hydrogen • The Lyman series emits in the ultraviolet region, the Balmer in the visible region, the Paschen in part of the infrared region, and the Brackett in another section of the infrared region. • Note: the emissions are “tied” to the energy level to which the electron is returning

34. Hydrogen Spectral Series

35. Bohr explains H spectra • Bohr focused primarily on the Balmer series of H • His theory and mathematics adequately explained these observed phenomena • Each of the lines in the line spectra corresponds to an electron absorption or emission as it moves from one orbit to another • The orbits are quantized

36. Energy changes of the electron • ∆E = Ef - Ei • = RH(1/ni2 - 1/nf2) • where ni is initial orbit and nf is final orbit • Since ΔE = hν • ∆E = hν = RH(1/ni2 - 1/nf2) • Take notice, the energy difference will be positive for an absorption in which the value of the final state will be greater than the initial state and the converse will be true

37. And so goes another model…. • Bohr’s mathematics and his model ran into trouble when working with complex atoms, those having more than one electron

38. Mechanics • Mechanics – branch of physics dealing with the forces creating changes in the motion of bodies • Classical mechanics – these are primarily the laws developed by Newton • -limited in their application – they pertain to objects of “normal” size (mass) traveling at typical velocities • - conflicted with the Bohr model of the atom where in which the electrons and the atom itself were quantized • smooth, continuous energy transitions would have been predicted by classical mechanics • Einstein’s relativistic mechanics applied to bodies near the speed of light, but generally not of extremely small mass • Wave or quantum mechanics was developed to work with the motion of subatomic particles; those traveling near the speed of light and having very small masses

39. Louis deBroglie • deBroglie suggests that matter has wave characteristics • After all, Planck and Einstein attached particle character to a wave • He assigns a wavelength to moving particles

40. Irwin Schrödinger • He establishes his mathematical work by focusing upon the electron as a wave rather than a particle • His work establishes points about the nucleus where the electron may be permitted to exist

41. Max Born • furthered Schrödinger’s work by determining the probability of finding an electron at those permissible points • Upon inspection, the points of higher probability form geometric shapes • These regions of high probability are called orbitals • This is a major shift from the Bohr atom in which the electron traveled in a limited circular pathway called an orbit

42. Werner Heisenberg’s Uncertainty Principle • The principle states that it is impossible to know the exact location and momentum of a particle (electron) at the same time. • Identifying the electron’s position requires an interaction with something like a photon. This interaction produces a change in the electron’s energy (momentum) and position.

43. Quantum numbers • Quantum Numbers for Electron Orbitals – these values provide information with regard to the orbitals that may “hold” an electron • It is similar to having an “address” for the orbital and hence the electron • n : the name is the principal quantum number • This quantum number refers to the energy level of the orbital. As n increases, the electron orbital becomes larger and the electron spends more time farther from the nucleus.  

44. Principal Quantum Number • Symbol is n • n may have integral values of n = 1, 2, 3... ∞ • This quantum number refers to the energy level of the orbital. • As n increases, the electron orbital becomes larger and the electron spends more time farther from the nucleus

45. Azimuthal or Orbital (orbital angular) Quantum Number • This quantum number’s values are dependent upon the value of n • It has a symbol of l • The azimuthal qnatum numbers are integral values of l = 0 to l = (n – 1). • This quantum number identifies the energy sublevel which in turn defines the shape of the orbital. • There are special letters assigned to each l value.

46. Corresponding energy sublevels

47. Orbital Types

48. Magnetic or Orientation Quantum Number • The symbol is ml • The are a set of ml values for each l value of a given energy level • Magnetic quantum numbers are integral values of ml = - l to + l including 0. • It refers to the orientation of the orbital in space about the nucleus.

49. Magnetic Q.N. cont’d • The number of ml values will also indicate how many orbitals make up a given sublevel. • This is always an odd number. • Therefore: s sublevel – one “s” orbital p sublevel – three “p” orbitals • d sublevel – five “d” orbitals • f sublevel – seven “f” orbitals 

50. s orbital