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. Wave particle duality

4. “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.

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

6. 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.

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

8. 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

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

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

11. Particles as “waves”DeBroglie • Rearranging

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

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

14. Explaining the electron • Continuous spectrum: Contains all the wavelengths of light. • Line spectrum: Contains only some of the wavelengths of light.

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

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

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

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

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

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

21. The Bohr Model

22. How does Planck’s Theory support Bohr’s “quantized orbit” • The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus

23. 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).

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

25. 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.

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

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

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

29. Quantum Model

30. 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.

31. 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.

32. Let’s say you have a room with flies flying around in it

33. The flies are not just anywhere in the room. They are inside boxes in the room.

34. You know where the boxes are, and you know the flies are inside the boxes, but…

35. you don’t know exactly where the flies are inside the boxes

36. The room is an atom The flies are electrons The boxes are orbitals

37. The room is an atom The flies are electrons The boxes are orbitals Science has determined where the orbitals are inside an atom, but it is never known precisely where the electrons are inside the orbitals

39. Hey, where am I?

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

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

42. 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

43. Letters are also used to represent the 2nd quantum number

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

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

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. So what are the sizes and shapes of orbitals?

48. The area where an electron can be found, the orbital, is defined mathematically, but we can see it as a specific shape in 3-dimensional space…

49. z y x

50. z y The 3 axes represent 3-dimensional space x