Atomic Structure and Periodicity

1. Atomic Structure and Periodicity Electronic structure of atoms from analysis of light emitted or absorbed by substances

2. Radiationenergy transmitted thru space in form of waves • Electromagnetic radiation • Has fundamental properties/behaves in predictable ways according to basics of wave theory • Called radiant energy (carries energy through space) • All move thru vacuum at speed of light (3.00 x 108 m/s) • Consists of • Electrical field (E) which varies in magnitude in direction perpendicular to direction in which radiation is traveling • Magnetic field (M) oriented at right angles to electrical field • Called transverse waves (disturbances perpendicular to direction of energy flow)

3. (wave is periodic disturbance)

4. Waves • Wavelength (distance between 2 adjacent parts of 2 waves) • Frequency (# complete wavelengths that pass given point each second) • Wavelength/frequency inversely proportional • Wave with shortest wavelength has highest frequency • Wave with longest wavelength has lowest frequency • Speed of light = (Wavelength)(Frequency): c = λν • c = 3.00 x 108 meters per second (m s-1), and is customarily measured in nanometers (nm, 1 x 10-9 m) • λ =wavelength (m) •  = frequency meters per second or hertz (Hz-s1)

5. Which wave has the higher frequency? • Lower wave has longer wavelength. Longer wavelength has lower frequency. B has higher frequency and a has lower frequency. • If one wave represents visible light and the other represents infrared light, which wave is which? • Infrared radiation has longer wavelength than visible light. A would be infrared radiation and b visible light. • Which is red light and which is blue light? • Red light has longer wavelength than blue, so a is red and b is blue.

7. Electromagnetic Spectrumall light has different amounts of energy Wavelength (m) Other units Frequency (Hz) Energy (eV) • Radio 3 km (1000) 1 x 108 4.1 x 10-7 • Microwave 2 x 10-2 mm/cm (10-2/-3) 1.5 x 1010 6.2 x 10-5 • Infrared 4 x 10-4 μm (10-6 ) 7.5 x 1011 3.1 x 10-3 • Visible 5 x 10-6 nm (10 -9) 6 x 1013 0.25 • Ultraviolet 1 x 10-7 3 x 1015 12.4 • X-ray 8 x 10-11 Å (10-10)3.75 x 1018 1.5 x 104 • Gamma-ray 2.5 x 10-12 1.2 x 1020 4.95 x105

8. T/F Questions: • Blue light has a shorter wavelength than red light. • True • X-rays have lower frequencies than radio waves. • False • Microwaves have higher frequencies than gamma rays. • False • Visible radiation composes the major portion of the electromagnetic spectrum. • False

9. Photosynthesis uses light with a frequency of 4.54 x 1014s-1. What wavelength does this correspond to? • c = λν • 3.00 x 108 m s-1 = λ(4.54 x 1014s-1) • 6.60 x 10-7m = 660 nm • Visible light goes from about 400 to 700 nm.

10. How electromagnetic radiation and atoms interactWave model of light cannot explain many aspects of light’s behavior • Emission of light from hot objects (called blackbody radiation because objects studied appear black before heating) • Emission of electrons from metal surfaces on which light shines (photoelectric effect) • Emission of light from electronically excited gas atoms (emission spectra)

11. Physicists in mid-1800s • Interested in interaction of light and matter • Source of radiant energy may emit single wavelength (monochromatic) • Most radiation sources produce radiation in many different wavelengths, which can be separated into components using prism • Continuous (emission) spectrum • Visible “white” light (incandescent) passed thru prism • Light separated into component colors • Forms continuous spectrum in which colors blend into each other

12. Line spectrum: Gas at low pressure is made incandescent Emitted light is not white When passed through prism, line spectrum is formed in which only specific colors of light are displayed Nature of colors depends on nature of gas Each element, when heated/sparked w/electricity, emits unique pattern of wavelengths (atomic spectra) used to identify them Line spectra of most elements/compounds very complex, but hydrogen is simple series of 4 lines () Spectroscope (spectrophotometer) Light observed by eye and information read by meter Shows line spectrum, not continuous one of white light Spectrogram: light detected by electron device and recorded on paper

14. infrared infrared infrared • Johannes Rydberg-extended Balmer’s equation so that all wavelengths could be predicted • He found similar series of lines in infrared (Paschen series) and ultraviolet (Lyman series) regions visible • Balmer (1885)-found empirical mathematical relationship between wavelength of lines he observed in visible region of line spectrum of hydrogen ultraviolet

15. Black body radiationQuantum Theory • Heated solids emit radiation • Usually in infrared, but visible radiation emitted if hot enough • Wavelength distribution depends on temperature • As temperature of object increases, color of emitted light changes from red-hot to white-hot as more blue light added • Prevailing laws of physics didn’t account for relationship between temperature/intensity/wavelengths of emitted radiation • Classical physics said object can acquire or lose any amount of energy no matter how small • But all attempts to explain wavelengths of electromagnetic radiation emitted by heated bodies using classical theory failed

16. (1900) Max Planck solved this Assumed energy can be released or absorbed by atoms only in discrete “chunks” of some minimum size Called smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation quantum (“fixed amount”) Total amount of energy absorbed or emitted by vibrating atoms occurred only in discrete multiples of frequency of vibration (increment of energy)

17. E = hν = hc/λ Energy of electromagnetic waves proportional to frequency/inversely proportional to wavelength E = nhν (n = 1, 2, 3…) h = minimum value of energy (quantum)  = frequency of radiation h = Planck’s constant (small value explains why we do not sense quantum nature of energy in our macroscopic world) = 6.626 x 10-34 J-s Energies are quantized 2hν , 3hν, etc. (2 or 3 quanta of energy emitted) You can’t be in between stairs on a staircase With this equation, Planck explained entire spectrum of radiation emitted by object at certain temperature

19. Einstein, Photoelectric Effect, and Photons • (1905) Photoelectric experiment showed energy of ejected electrons proportional to frequency of illuminating light • Interaction must be like that of particle giving its energy to electron • Fit with Planck’s hypothesis that light in blackbody radiation experiment could only exist in discrete bundles of energy • This particle nature of light was solution to problems physicists encountering about nature of light • Planck/Einstein showed light had wavelike/particle-like properties (dual nature of light)

20. Light shining on clean metal surface causes surface to emit electrons • Each metal has minimum frequency of light below which no electrons emitted • Einstein assumed that radiant energy striking metal surface does not behave like wave but as photons (tiny packets of energy) • Each photon must have energy equal to Planck’s constant times frequency of light • Energy of photon = E = hν • Radiant energy is quantized • Photon strikes metal surface and is absorbed, transferring energy to electron in metal • If sufficient energy, electron emitted from metal energy wavelength

21. Example • What are the frequency and the energy of blue light that has a wavelength of 400 nm? • (400 nm)(ν) = 3.00 x 108 m s-1 • (400 x 10-9 m)(ν) = 3.00 x 108 m s-1 • 7.5 x 1014 s-1 • E = hν = 6.62 x 10-34 J s)(7.5 x 1014 s-1) • 4.96 x 10-19 J)

22. Niels Bohr (1913) • Completed theory of how H atom constructed • Took quantum theory/Rutherford’s model of nucleus to predict that electrons orbit nucleus at specific, fixed radii, like planets orbiting sun • Solar system model-duplicated Rydberg equation from fundamental constants already known and explained that electrons exist in only certain “allowed orbitals” • Classical physics says that a charged particle moving in circular path should continuously lose energy by emitting electromagnetic radiation • Electron should then spiral into positive nucleus • Worked for atoms and ions with one electron, but not for more complex atoms

23. Based model on three postulates: Only orbits of certain radii, corresponding to certain definite energies, are permitted for electron in hydrogen atom. Electron in permitted orbit has specific energy and is in “allowed” energy state. Electron in allowed energy state will not radiate energy so it won’t spiral into nucleus. Energy emitted/absorbed by electron only as electron changes from one allowed energy state to another. Energy emitted/absorbed as photon, E = hν Levels with lowest energy-ground state (closest electron could approach hydrogen nucleus) Any higher level-excited state

25. Bohr Model Limitations Importance Electrons exist only in certain discrete energy levels, described by quantum numbers Energy involved in moving electron from one level to another • Cannot explain spectra of atoms other than hydrogen, except crudely • Didn’t explain problems of electron falling into nucleus

26. Related energy levels to observed wavelengths emitted by hydrogen atom E = -2.178 x 10-18 J [Z2/n2] E = energy (in Joules) Z = nuclear charge (1 for H’s one proton) n = integer related to orbital position Farther out from nucleus, higher value of n If electron is given enough energy, it goes away from nucleus (ionized and n = ∞) Lowest energy state is n = 1, ground state Highest energy state is n = ∞, ionized

27. Calculate the energy corresponding to the n = 3 electronic state in the Bohr hydrogen atom. • E = -2.178 x 10-18 J [Z2/n2] • E3 = -2.178 x 10-18 J [(1)2/32] • = 2.42 x 10-19 J

28. Calculate the energy change corresponding to the excitation of an electron from the n = 1 to n = 3 electronic state in the hydrogen atom. • ∆E = Efinal – Einitial = E3 – E1 • You can calculate both and then subtract or • E = -2.178 x 10-18 J [Z2/n2] • E = -2.178 x 10-18 J [1/32 – 1/12] • = E = -2.178 x 10-18 J [-8/9] • +1.936 x 10-18 J • Energy was absorbed to excite electron, so system gained energy

29. What wavelength of electromagnetic radiation is associated with the energy change in promoting an electron from the n = 1 to n = 3 level in the hydrogen atom? (use ∆E value from last example) • ∆E = hc/λ so λ= hc/∆E • λ= 6.626 x 10-34 J s (2.9979 x 108 m/s) 1.936 x 10-18 J • = 1.26 x 10-7 m • = 102.6 nm

30. Homework: Read 7.1-7.4, pp. 289-304 Q pp. 337-338, #39, 40, 42, 43, 44, 46, 48, 52, 54, 56, 58

31. Wave Behavior of Matter Dual nature of radiant energy

32. All matter has wave characteristics Sometimes behavior of electrons is better described in terms or waves than particles Simple relationship between electron’s wave and particle characteristics Louis de Broglie (1924) h = 6.63 x 10-34 joule-sec momentum

33. Werner Heisenberg (1920s) • Discovery of wave properties of matter raised questions about classical physics • Ball rolling down ramp: using equations of classical physics, we can calculate ball’s position, direction of motion, and speed at any time, with great accuracy • Can we do same for electron which exhibits wave properties? • Wave extends in space so its location not precisely defined • So impossible to determine exactly where electron is located at specific time • Heisenberg proposed that dual nature of matter places fundamental limitation on how precisely we can know both location and momentum of any object • Limitations due to very small masses of electron

34. Heisenberg Uncertainty Principle • Position and momentum of any particle cannot be known exactly at same time • When radiation used to locate particle hits it, it changes its momentum • So position/momentum cannot both be measured exactly • As one known more precisely, other becomes less certain • ∆x ▪ ∆(mv) ≥ h/4π • ∆x = uncertainty in particle’s position • ∆(mv) = uncertainty in particle’s momentum • h = Planck’s constant • Smallest possible uncertainty is h/4π

35. We cannot know exact location of electron around atom at any given time • We can know probability of it being within certain region • Probability distribution • Square of wave function • Represents probability (statistical likelihood) of finding electron at particular area around nucleus • Limit of size of orbital is radius of sphere that encloses 90% of total electron probability • 90% probability of finding electron in that orbital • Electron orbitals don’t represent specific orbits like those of planets but is probability function describing possibility that electron will be found in region of space

36. Erwin Schrödinger (1927) • Wave-mechanical theory • Applied equation for waves to electrons in atoms • Electron is assumed to behave as a standing wave • Only certain orbits shaped so “wave” (electron) can fit • He was not certain that treating electron as wave would make any sense • Position of electron in wave • Mechanical model described by probability of where it will be located • Wave function of electron represents allowed coordinates where electron may reside in atom • Each wave function is called an orbital

37. Electron looping around nucleus in hydrogen atom according to classical physics Electron probability density cloud of hydrogen atomaccording to quantum mechanics (Schrödinger)

38. Quantum Numbers Three coordinates used to describe various properties of orbital in which electrons are found

39. Orbitals • Wave functions/corresponding energies for electrons • Each orbital describes specific distribution of electron density in space, as given by orbital’s probability density • Each orbital has characteristic energy and shape • Node – intermediate point at which probability of finding electron there is zero

40. n = Principle Quantum Number • Describes size of orbital • Energy levels, n = 1-7 (or K  Q) • Further away from nucleus, higher #/energy • Maximum number of electrons in any one level is 2n2 • Principal quantum number n = subshells n

41. l = Angular Momentum Quantum Number • Describes shape of subshells or orbitals within each energy level • Ranges from 0 to n-1 (l = n-1) • Electrons fill from lowest to highest energy

42. ml = Magnetic Quantum Number • Relates to the magnetic field generated by electron with angular momentum. • Only one way for sphere to be oriented in space. • Polar or cloverleaf shapes can point in different directions. • m describes orientation in space of particular orbital. • Called magnetic because effect of different orientations of orbitals first observed in presence of magnetic field. • May be - l, + l.

43. ms = Magnetic Spin Quantum Number • Relates to intrinsic magnetism of electron itself (spinning charge produces magnetic field) • May be either –½ or +½ • Pauli Exclusion Principle: no two electrons in given atom can have same set of four quantum numbers

44. Principal Quantum Numbers

45. s = “sharp,” p = “principle,” d = “diffuse,” f = “fundamental” From early spectral line studies, before quantum #s

47. If each orbital can hold a maximum of 2 electrons, how many electrons can each of the following subshells hold? • 2s • 2s  l = 0, ml = 0 (1 value) x 2 electrons = 2 • 5p • 5p  l = 1, ml = +1, 0, -1 (3 value) x 2 electrons = 6 • 4f • 4f  l = 3, ml = +3, +2, +1, 0, -1, -2, -3 (7 value) x 2 electrons = 14 • 3d • 3d  l = 2, ml = +2, +1, 0, -1, -2 (5 value) x 2 electrons = 10 • 4d • Same as 3d

48. Which of the following sets of quantum numbers are not allowed? • n = 1, l = 0, ml= 1 • Not allowed-ml can’t be greater than • n = 2, l = 2, ml= 1 • Not allowed-l can’t be greater or equal to n) • n = 5, l = 3, ml= 2 • Allowed • n = 6, l = -2, ml= 2 • Not allowed-l can’t be negative • n = 6, l = 2, ml= -2 • Allowed

49. Which of the following sets of quantum numbers are not allowed? • n = 3, l = 3, ml= 0, ms= -½ • Not allowed-l cannot be equal to n • n = 4, l = 3, ml= 2, ms= +½ • Allowed • n = 4, l = 1, ml= 1, ms= -½ • Allowed • n = 2, l = 1, ml= -1, ms= -1 • Not allowed- msmust be either +½ or –½ • n = 5, l = -1, ml= 2, ms= +½ • Not allowed-l must be positive integer • n = 3, l = 1, ml= 2, ms= -½ • Not allowed-ml must be between –l and +l • n = 3, l = 2, ml= -1, ms= 1 • Not allowed- msmust be either +½ or –½

50. Homework: Read 7.5-7.8, pp. 304-312 Q pp. 338-339, #60, 62, 64, 66