Atomic Structure & Periodicity

1. Atomic Structure & Periodicity Chapter 7

2. Early 1900’s • Rutherford model detailed nucleus plus electrons moving around. • Did not explain HOW electrons occupied that space

3. Questions about Electrons • Chlorine, Argon, Potassium are found in order on periodic table • Why do they react so differently? • Chlorine is yellow-green gas, poisonous, and reacts with many other elements • Potassium is a highly reactive metal (solid) • Argon is unreactive (inert) gas • Why?

4. Some Answers • Some answers were provided by the light emitted by different elements when heated in a flame. • There is a relationship between electrons and light emissions.

5. Review – The Wave Nature of Light • Electromagnetic Radiation – a form of energy • Exhibits wave-like behavior as it travels through space • Visible light is PART of the EM spectrum The EM Spectrum

6. Amplitude (Rest) Characteristics of EM Radiation • Wavelength – distance between 2 waves • Frequency – waves per second (herz) • Amplitude –Height of wave • Speed – 3.0x108 m/s in a vacuum

7. EM Characteristics Relationships • C =  • C = speed of light (a constant) •  (lambda) = wavelength in meters •  = frequency in waves per second • If wavelength goes up, frequency goes down. • If frequency goes up, wavelength goes down

8. Example Problem • A microwave of 3.44 x 109 Hz is used to send information. What is the wavelength? • C =  • C = 3.00 X 108 m/s •  = 3.44 x 109 Hz (waves/sec) •  = ?? m •  = C/  = 3.00 x 108 m/s = .872 x 10-1 = .0872m 3.44 x 109 1/s

9. Planck’s Constant • Planck went further and quantified a ‘quanta’: • E = h • E = Energy • h = Planck’s constant (6.626 x 10-34 J) •  = frequency • Planck’s Theory: matter can absorb or emit energy only in whole number multiples of h, like 1 h, 2 h, 3 h, etc.

10. Photoelectric Effect • Planck’s Theory did not explain the photoelectric effect: • When certain wavelengths of light shine on a metal, electrons (called photoelectrons) are emitted. How can this happen? • This is the principal used by photocells in your calculators • This suggested that light was particles not waves • Something must be hitting the electrons for them to bounce out….

11. Einstein and the Dual Nature of Light • 1905, Albert Einstein extended Planck’s theory to include BOTH wavelike and particle nature of light • A ‘photon’ a particle of light with no mass carries energy • Energy of a photon depends on its frequency • Ephoton = h

12. Atomic Emission Spectra • The set of frequencies of EM radiation emitted by atoms of the elements • Each element’s spectra is unique (one and only) • Because only certain colors of light are displayed, this means only certain frequencies are emitted. • This means that only photons with specific energies are emitted • Supports Planck’s Theory, but not classical physics theory of that time.

13. Atomic Emission Spectra

14. Quantum Theory and the Atom Section 2

15. Bohr Model of the Atom • Observed: hydrogen only emits certain frequencies of light • Niels Bohr (Danish) proposed a quantum model for the atom: • Lowest energy level allowed for an electron is its ‘ground state’ • When atom gains energy, electron goes to a higher level, an ‘excited state’. • The electron can have many ‘excited’ states

16. Bohr Model (Cont.) • Each energy level corresponds to one quanta of energy • Bohr model correctly predicted the emission spectra for hydrogen.

17. Bohr Atomic Model

18. Explaining the Hydrogen Line Spectrum • When energy is added, electron moves to a higher-energy orbit (from n = 1 to n = 2) • When atom moves back to lower-energy orbit, a ‘photon’ of energy is released • Energy release is equal to the frequency of the light spectrum. • Because only certain atomic energies are possible (certain orbits), only specific frequencies are emitted.

19. Energy and Atoms • Higher Energy Orbit Lower Energy Orbit • Specific distance • Specific amount of energy (quanta) • Specific frequency • Specific frequency = specific color

20. Bohr Atomic Model • Bohr model failed to explain the spectra of any other element • It was later determined that the Bohr model was fundamentally correct.

21. Quantum Mechanical Model • 1920’s – DeBroglie (French) Experiments • Electron orbits behaved like waves, could they have multiple frequencies? • Could particles, including electrons, behave like waves? • If an electron has a wavelike motion AND is restricted to circular orbits of fixed radius, the electron is allowed only certain wavelengths

22. Quantum Mechanical Model • DeBroglie Equation •  = h/mv • Predicts that ALL moving particles have wave characteristics • Auto moving at 25 m/s, with mass 910kg has a wavelength of 2.9x10-38 (way too small to be detected) • Electron at same speed has a wavelength of 2.9x10-5 (easily measured) • About the same spacing as atoms in a crystal

23. DeBroglie & Heisenberg • Work on wave equations and electrons resulted in: • Electrons bound to the nucleus resemble a standing wave • Started working on the wave mechanical properties of the electrons. • Standing waves occur in musical instruments (strings are easiest to see/understand) where interference patterns are created by waves reflecting back from ends • Standing waves only occur in whole number multiples of the original wave.

24. DeBroglie & Heisenberg • If electrons behave like waves AND can only exist in whole number multiples: • Electrons can have multiple frequencies in the same orbital, but only whole number multiples of the ground state. • Explains quantized energy.

25. Multiples of Wavelengths

26. Wavelengths in Orbits

27. DeBroglie’s Findings • Notice also that this means the electron does not exist at one single spot in its orbit, it has a wave nature and exists at all places in the allowed orbit. And the Bohr atom really looks like the following diagram:

28. Schrödinger Wave Equation • 1926 Erwin Schrödinger (Austria) furthered the theory. • Created an equation that treated the hydrogen atom’s electron like a wave • New model applied equally well to other atoms • This body of knowledge became the “quantum mechanical model of the atom”

29. Schrodinger Equation • H Ψ = E Ψ • H = mathematical ‘operator’ • Ψ = coordinates of electron’s position in 3-D space • E = total energy of the electron • Equation results in many solutions • So Ψ really represents an electron orbital

30. Just For Reference… The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is given by where i is the imaginary unit,         is the time-dependent wavefunction,    is h-bar, V(x) is the potential, and      is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts using separation of variables     to write thus obtaining Setting each part equal to a constant then gives And so on and so on…..

31. More Evidence of Waves • Diffraction patterns (rainbows) occur when light hits a regular array of points or lines • CD/DVD grooves result in prism effect.’ • Xrays through a sodium chloride crystal produce a diffraction pattern. • Can only happen with waves providing an interference pattern of high and low troughs

32. What does this mean about electron orbits? • Atomic orbitals are NOT Bohr orbitals! • Atomic orbits are 3-dimensional regions around the nucleus (like a fuzzy cloud). • Where exactly is the electron? • We don’t know!

33. Heisenberg Uncertainty Principle • It is impossible to make any measurement on an object without disturbing the object at least a little; • States: • That is is fundamentally impossible to know precisely both the velocity and the position of a particle at the same time. • Mathematically: ΔX = particle position uncertainty Δ(mv) = momentum uncertainty H = Plank’s constant

34. Heisenberg Uncertainty Principle • Minimum uncertainty is 4Ψ • More accurately we know particle’s position, less accuracy is known about momentum. • More accurately we know particle momentum, less accurately we know particle position

35. Heisenberg Uncertainty Principle

36. What Does This Mean? • The squared wave function provides a ‘relative probability’ of finding an electron at a particular position. Therefore, if N1 is position 1 and N2 is position 2, the relative probabilities of finding an electron at a particular position is N1/N2 • This gives us an electron density (or electron probability) map Which shows us an electron ‘cloud’ of probabilities. • Also gives us a probability of finding an electron a certain distance from the nucleus

37. Electron Probability Graphs

38. What Does This Mean about Electron Orbitals • If you use Schrodinger equation for hydrogen, you find many wave functions (orbitals) that satisfy it. • Each orbital is characterized by a series of numbers called QUANTUM NUMBERS. • Quantum numbers describe properties of the orbitals. • Principal quantum numbers are assigned to indicate relative size and energy of orbitals • (n) – principal quantum number – has integer values 1, 2, 3,… • As n increases, orbital gets larger, has more energy, is less tightly bound to nucleus, energy is less negative; • Up to 7 energy levels have been detected for hydrogen • As (n) increases, orbital is larger and electron spends more time further from nucleus

39. What Does This Mean about Electron Orbitals • Angular Momentum number (l) has integer values from 0 to n-1 for each value of n • This quantum number is related to the shape of the orbital • l = 0 is s • l = 1 is p • l = 2 is d • l = 3 is f

40. What does this mean about electron orbits? • Each principal energy level can have sublevels • Principal energy level one has only one sublevel • Principal energy level 2 has 2 sublevels • Principal energy level 3 has 3 sublevels • And so on..

41. What does this mean about electron orbits? • Sublevels are labeled s, p, d, or f according to their shape • s sublevels are spherical • p sublevels are dumbell shaped • d sublevels and f sublevels are not all shaped the same. • Each orbital can have at most 2 electrons

42. What does this mean about electron orbits? • Principal level one has only ONE sublevel • Designated as 1s (spherical) • 2 total electrons (2 elements in 1st row) • Principal level 2 has 2 sublevels • Designated as 2s and 2p • 2s is spherical (like 1s) but larger • 2p has three dumbbell shaped orbitals on each of three axis • Total 8 electrons (8 elements)

43. What Does This Mean about Electron Orbitals • Magnetic Quantum Number (ml) : • Related to orientation of orbital in space relative to other orbitals of the atom • Has integer values between l and –l, including zero. • Quiz: For Principal quantum level n=5, list all allowed subshells and give designation of each: • l=0 l=1 l=2 l=3 l=4 • 5s 5p 5d 5d 5f

44. What Does This Mean about Electron Orbitals • Review: an orbital can best be represented by a probability distribution, or by an area that surrounds 90% of the probability areas • Areas between areas of high probability have probability of zero • These are called nodal surfaces, or nodes • Nodes increase as n increases • For s orbitals, these resemble spherical shapes • For p orbitals have ‘lobes’ labeled along the xyz axes. • Very complex orbital probability distribution

45. What does this mean about electron orbits?

46. What does this mean about electron orbits? Note p orbital alignment along the xyz axes

47. What does this mean about electron orbits? Note: d orbitals are BETWEEN the xyz axes.

48. What Does This Mean about Electron Orbitals • Energy of a particular Electron orbital is determined only by its value of n. • All orbitals with same value of n have the same energy (said to be degenerate)

49. Electron Spin and Pauli Principle • First postulated by Goudsmit and Uhlenbeck at University of Leyden (Netherlands) • A fourth quantum number was necessary to account for details in the emission spectrum of atoms • Spectral data indicates a magnetic moment with two possible orientations. • Assumed an electron could have 2 possible spin states • Lead to electron spin quantum number (ms) • Electron spin can only have 2 values: +½ and –½ • Significance given by Pauli exclusion principle: in a given atom, no two electrons can have the same 4 quantum numbers (n, l, ml and ms • Since an orbital can only have 2 electrons, they must have opposite spins

50. Review • Each principal energy level can have the same number of sublevels as the level number • Each sublevel orbital has a different shape • Each orbital can have only 2 electrons • What does this mean?