Electrons – the early years

1. Electrons – the early years

2. Electromagnetic Radiation • Radiant energy that travels through space at the speed of light in a vacuum.

3. An Electromagnetic Wave

4. The Electromagnetic Spectrum Communications involve longer wavelength, lower frequency radiation. UV, X-rays are shorter wavelength, higher frequency radiation Visible light is a small portion of the spectrum.

5. Wave particle duality

6. “Light as a wave” • Waves have 3 primary characteristics: • 1. Wavelength: distance between two peaks in a wave. • 2. Frequency: number of waves per second that pass a given point in space. • 3. Speed: speed of light is 2.9979  108 m/s.

7. Wavelength and frequency are inversely proportional •  • = c •  = frequency [s1 ; hertz (Hz)] •  = wavelength (m) • c = speed of light (m/s)

8. Light as a “particle”Photoelectric Effect The photoelectric effect occurs when photons of sufficient energy actually kick electrons off of the surface being struck by light.

9. Light as a “particle”Max Planck Transfer of energy is quantized, and can only occur in discrete units, called quanta.

10. Planck’s Constant • E = change in energy, in J • h = Planck’s constant, 6.626  1034 J s •  = frequency, in s1 •  = wavelength, in m

11. Light as a “particle”Energy and Mass (Einstein) E = mc2 • E = energy • m = mass • c = speed of light

12. Particles as “waves”DeBroglie • Einstein & Planck

13. Particles as “waves”DeBroglie • Rearranging

14. Particles as “waves”DeBroglie • For a “generic” particle (not EMR)

15. deBroglie’s Equation •  = wavelength, in m • h = Planck’s constant, 6.626  1034 J• s • m = mass, in kg •  = velocity, in m/s

16. Explaining the electron • Continuous spectrum: Contains all the wavelengths of light.

17. Explaining the electron • Line spectrum: Contains only some of the wavelengths of light.

18. Explaining the electron • When a sample of an elemental gas is electrified it emits electromagnetic radiation

19. Explaining the electron • When viewed through a diffraction grating, each element produces a distinctive line spectrum

20. Hydrogen’s Line Spectrum(Balmer series – visible)

21. Hydrogen’s Line SpectrumUV, Visible, Infrared)

22. The Bohr Model The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits (quantized energy states.)

23. The Bohr Model “Orbits” are determined by distance from nucleus where orbit circumference is a whole number multiple of the deBroglie wavelength.

24. The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus

25. The Bohr Model

26. The Bohr Model The energy of the orbits increases with distance from the nucleus. Ground State: The lowest possible energy state for an atom (n = 1).

27. The Bohr Model An electron can absorb energy and “jump” from its ground state to a higher energy orbit (excited state).

28. The Bohr Model Electrons will not remain in an excited state. Electrons emit energy in the form of photons so that they can return to the ground state. These photons make up the line spectrum.

29. Each circle represents an allowed energy level. The Bohr Model Emission: atom gives off energy (as a photon) An electron drops to a lower energy level. Excitation: atom absorbs energy that is exactly equal to the difference between two energy levels. An electron attains a higher energy level.

30. The Bohr Model The frequency of the lines depends on the size of the “jump”.

31. The Bohr Model • E = energy of the levels in the H-atom • z = nuclear charge (for H, z = 1) • n = an integer

32. Energy Changes in the Hydrogen Atom • E = Efinal stateEinitial state • ∆E = -2.178x 10-18J [1/nf2 – 1/ni2]

33. Problems with Bohr’s Model • Only explains hydrogen atom spectrum • and other 1 electron systems • Neglects interactions between electrons • Assumes circular or elliptical orbits for electrons - which is not true

34. Quantum Model

35. Quantum Mechanics • Based on the wave propertiesof the atom •  = wave function • = mathematical operator • E = total energy of the atom • A specific wave function is often called an orbital.

36. Heisenberg Uncertainty Principle • x = position • mv = momentum • h = Planck’s constant • The more accurately we know a particle’s position, the less accurately we can know its momentum.

37. Probability Distribution • square of the wave function (ψ2) • probability of finding an electron at a given position

38. Quantum Numbers (QN) • 1. Principal QN • (n = 1, 2, 3, . . .) - related to size and energy of the orbital. • Defines an energy level or “shell”

39. Quantum Numbers (QN) • 2. Angular Momentum QN • (l = 0 to n 1) - relates to shape of the orbital. • n and l together define a sublevel or subshell

40. Quantum Numbers (QN) • 3. Magnetic QN • (ml = l to  l ) - relates to orientation of the orbital in space relative to other orbitals.

41. Quantum Numbers (QN) • 4. Electron Spin QN (ms= +½,  ½) - relates to the spin states of the electrons.

42. S orbitals

43. P orbitals

44. D orbitals

45. f orbitals

46. Pauli Exclusion Principle • In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml , ms). • Therefore, an orbital can hold only two electrons, and they must have opposite spins.

47. Aufbau Principle “electrons are lazy” • the number of electrons in an atom is equal to the atomic number; • each added electron will enter the orbitals in the order of increasing energy

48. Hund’s Rule “electrons don’t like each other” • every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

49. Summary

50. Orbital Notation • draw a box / line for each orbital. • Remember that s, p, d, and f subshells contain 1, 3, 5, and 7 degenerate (equal energy) orbitals, respectively. • Remember that an orbital can hold 0, 1, or 2 electrons only • If there are two electrons in the orbital, they must have opposite (paired) spins (Pauli principle )