Chapter 6 Electronic Structure of Atoms

1. Chapter 6Electronic Structureof Atoms or “How I Learned to Stop Worrying and Love the Electron”

2. Problems with the Rutherford Model • Classical physics says atoms should emit light and destroy themselves - they don’t • Atoms can be induced to emit light, but they give off a line spectrum, rather than a continuous spectrum. • Every atom gives off different colours of light. • No explanation of why different atoms have different properties, or the same properties.

3. Let’s Talk About Light

4. What is Light? • light is radiant energy. • a better term is electromagnetic energy (EMR) • includes not only visible light, but many forms of EMR we cannot see directly: • heat • microwaves • x-rays • light has properties of both waves and particles.

5. Wave model of Light • The distance between corresponding points on adjacent waves is the wavelength • The symbol is the Greek letter lamda(). • The height of the wave is the amplitude. It corresponds to the intensity of the light

6. Waves • The number of waves passing a given point per unit of time is the frequency, • The symbol is the Greek letter nu (). • The longer the wavelength, the smaller the frequency.

7. Electromagnetic Radiation • EMR is a continuous spectrum of wavelengths.

8. Using λ and ν to determine “colour” • “Colour” is a term used to describe visible light. • Visible light is a very small part of the electromagnetic spectrum: • radio waves -- ultraviolet • microwaves -- x-rays • infrared -- gamma rays • visible

10. Colour of Light • we can identify light by its wavelength or frequency: • a wave 5.00 x 10-7 m is • green • a wave 6.80 x 10-7 m is • red • a wave 2.60 x 10-5 m is • infrared • a wave 7.80 x 10-10 m is • in the x-ray region.

11. Speed of Light • is the one thing that is constant in the universe (sort of). • in a vacuum, the speed of light is 3.00 x 108 m/s • there is a relationship between wavelength and frequency: • where • c = speed of light • λ = wavelength • ν = frequency

12. Complete questions 6.13 to 6.18, even

13. Quantized Energy and Photons • The wave model of light is good, but it does not explain: • how an object can glow when its temperature increases. (Blackbody radiation) • emission of electrons by shining light on the surface of a metal. (photoelectric effect) • emission of light from electrons of excited gas atoms. (emission spectra)

14. Blackbody Radiation • Heated solids emit radiation (blackbody radiation) • The wavelength distribution depends on the temperature (i.e., “red hot” objects are cooler than “white hot” objects). • Why does wavelength or frequency depend on temperature? • Max Planck suggested a way out by assuming that energy comes in packets called quanta.

15. Planck proposed a relationship between energy and the frequency of light quanta: • where: • E = energy in Joules • h = Planck’s constant (6.6262 x 10-34 J·s) • ν = frequency, in Hertz (1/s, s-1) • as energy increases, so does frequency.

16. Complete questions 6.21 to 6.28

17. The PhotoelectricEffect

18. Photons • Einstein used the quantum to explain the photoelectric effect: • Light comes in particles, called photons. • The energy of each photon is determined by Planck’s equation. • Light shining on the surface of a metal can cause electrons to be ejected from the metal.

19. The electrons will only be ejected if the photons have sufficient energy: • Below the threshold frequency no electrons are ejected. • Above the threshold frequency, the excess energy appears as the kinetic energy of the ejected electrons. • Light has wave-like AND particle-like properties. • Complete question 6.30

20. Line Spectra and the Bohr Model Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

21. The Nature of Energy • A white light source produces a continuous spectrum, like a rainbow. • When elements are excited, only a line spectrum of discrete wavelengths is observed.

22. Hydrogen Spectrum • has line spectra in 3 regions of the EM Spectrum: • Ultraviolet – Lymann Series • Visible – Balmer Series • Infrared - Paschen Series

23. The Nature of Energy • Niels Bohr adopted Planck’s ideas about the quantum and applied them to the electrons around a nucleus.

24. The Nature of Energy • Bohr’s model is based on three postulates: • Electrons in an atom can only occupy certain permitted orbits, or quanta. • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. • Energy is only absorbed or emitted to move an electron from one “allowed” energy state to another; the energy is emitted by a photon: E = h

25. The Nature of Energy • An electron in its lowest permissible energy is at ground state • If an electron accepts a quantum of energy it will move to a higher energy level, or excited state. • When the electron moves back down to ground state it emits a photon of light of a frequency which correlates to the energy of the quantum.

26. 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.

27. this explains the line spectra of hydrogen: • Lyman series. High energy, in the UV range. Represents energy transition from higher quanta to ground state. • Balmer series. Intermediate energy, in the visible range. Represents energy transition from higher quanta to quantum 2. • Paschen series. Low energy, in the IR range. Represents energy transition from higher quanta to quantum 3.

28. Limitations of Bohr Model • cannot explain the spectra of atoms other than hydrogen. • However, the model introduces two important ideas: • The energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers. • Energy gain or loss is involved in moving an electron from one energy level to another.

29. h mv  = The Wave Nature of Matter • 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

30. What does this mean? • electrons have wave properties. • the orbits of electrons are multiples of the electron wavelength • the first orbit has a circumference of 1 λ, the second is 2 λ , etc.

31. The Uncertainty Principle • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known. • Our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

32. 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.

33. The wave function describes the electron’s matter wave; it gives the probability of finding the electron. • Electron density is another way of expressing probability. • A region of high electron density is one where there is a high probability of finding an electron.

37. Orbitals and Quantum Numbers • 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.

38. Principal Quantum Number, n • describes the energy level on which the orbital resides. • The values of n are integers ≥ 0. • correspond to the periods on the Periodic Table.

39. Azimuthal Quantum Number, l • defines the shape of the orbital. • Allowed values of lare integers ranging from 0 to n − 1. • letter designations communicate the different values of land, therefore, the shapes and types of orbitals.

40. Azimuthal Quantum Number, l • Theoretical g, h, i, etc. orbitals exist, but no atoms have been created to use them.

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

42. Magnetic Quantum Number, ml • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells. • Each subshell is designated by a number and a letter. • For example, 3p orbitals have n = 3 and l = 1.

43. In Summary

44. s Orbitals • Value of l = 0. • Spherical in shape. • Radius of sphere increases with increasing value of n.

45. p Orbitals • Value of l = 1. • Have two lobes with a node between them. • The letters correspond to allowed the values of ml of –1, 0, and +1.

46. d Orbitals • Value of l is 2. • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. • The letters correspond to allowed the values of ml of -2, –1, 0, +1 and +2.

47. forbitals • Value of l is 3. • 7 possible shapes, including 8 lobes and 2 doughnuts. • The letters correspond to allowed the values of mlof -3, -2, –1, 0, +1, +2 and +3.

48. Energies of Orbitals • Orbitals of the same energy are degenerate.

49. Spin Quantum Number, ms • two electrons in the same orbital do not have exactly the same energy. • The “spin” of an electron describes its magnetic field, which affects its energy.

50. Spin Quantum Number, ms • There is a spin quantum number, ms. • has only 2 allowed values: +1/2 and −1/2.