#### Transcript AP Chemistry Notes Quantum Theory and Atomic Structure

Quantum Theory and Atomic Structure AP Chemistry Late 1880s…physicists thought they knew everything…discouraged students from studying physics in college CLASSICAL THEORY OF PHYSICS MATTER ENERGY -particulate -massive -continuous -wavelike Background: WAVES Waves A disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacement of the medium itself. Parts of A Wave node peak/crest trough wavelength distance between two consecutive peaks or troughs in a wave symbol: lambda, l units: meters (m) frequency the number of waves passing a point in a given amount of time symbol: nu, n units: cycles/sec, 1/sec, sec-1, Hertz (Hz) Figure 7.1 Frequency and Wavelength c=ln Figure 7.2 Amplitude (Intensity) of a Wave Speed of radiation = wavelength · frequency c=l•n where c = 3 X 108 m/s (speed of light, all EM radiation in a vacuum) Electromagnetic Radiation The Electromagnetic Spectrum Sample Problem 7.1 Interconverting Wavelength and Frequency PROBLEM: A dental hygienist uses x-rays (l= 1.00A) to take a series of dental radiographs while the patient listens to a radio station (l = 325cm) and looks out the window at the blue sky (l= 473nm). What is the frequency (in s-1) of the electromagnetic radiation from each source? (Assume that the radiation travels at the speed of light, 3.00x108m/s.) Energy as a Wave Diffraction of Light Change in the directions and intensities of a group of waves after passing by an obstacle or through an aperture (slit) whose size is approximately the same as the wavelength of the waves Figure 7.4 Different behaviors of waves and particles. Prism used to separate light into wavelengths A single point source and the resulting wave fronts The diffraction pattern caused by light passing through two adjacent slits. Figure 7.5 Wave interference pattern produced by two point sources Constructive Interference Stadium waves Destructive Interference http://www.youtube.com/watch?v=P_rK66GFeI4 Young’s Double Slit Exp. (1802) Confirms that light is an electromagnetic wave Energy as a PARTICLE • Heat a solid and it starts to glow Hot coals ~1000 K Electric heating coil ~1500 K Lightbulb filament~2000 K • Why does the wavelength change with Temp? Max Planck (1903) - black body radiation Black body: a perfect absorber of radiation; object appears Black when cold and emits a temperature dependent spectrum of light Observations: Energy is gained and lost in whole numbers Intensity and frequency (color) of radiation depend on temperature Snow is a black body for IR radiation, but not for visible Energy as a PARTICLE • Heat a solid and it starts to glow Hot coals ~1000 K Electric heating coil ~1500 K Lightbulb filament~2000 K • Why does the wavelength change with Temp? • If an atom can only absorb certain wavelengths of energy, then it can only emit certain wavelengths Planck’s Quantum theory of EM waves Light energy is transmitted in discrete “packets” (photons) called quanta (singular is quantum) The energy of one quantum: E=hn h = Planck’s constant 6.63 x 10-34 J·s Niels Bohr and Max Planck at MIT “Photoelectric Effect” Einstein (1905) When EM radiation above a certain frequency is shined on the device, an electric current registers on the meter As frequency increases, the current increases BUT – below the cutoff frequency, no current is obtained, even at very high intensities!! Conclusion: Photon is a “particle” of light with energy E=hn Sample Problem 7.2 Calculating the Energy of Radiation from Its Wavelength PROBLEM: A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm. What is the energy of one photon of this microwave radiation? Planck and Einstein at Nobel Conference Dual Nature of Light Light has both: wave nature particle nature ATOMIC THEORY Determination of the Structure of the Atom 1897- J.J. ThompsonCathode Ray Tube Determined the charge/mass ratio of an electron. Suggested plum pudding model for atom 1911- Ernest RutherfordGold Foil Experiment Suggested presence of a positively charged nucleus Rutherford and Geiger. Figure 7.8 The line spectra of several elements Colors of “neon” lights Red = Ne Others = Ar, Hg, phosphor Continuous Spectrum vs. Line Spectrum Niels Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • The e-’s energy correspond to orbits around the nucleus. Outer orbits have higher energy • Photon E=hn light is emitted as e- moves from higher energy level to lower energy level Ground State: n = Excited State: n Ionized: n= 1 >1 ∞ Figure 7.10 Quantum staircase E = hn E = hn Problem – model does not work for atoms with more than 1 e- !!! Rydberg equation 1 l = R 1 n12 1 n22 R is the Rydberg constant = 1.09 × 107m-1 Figure 7.9 Three series of spectral lines of atomic hydrogen for the visible series, n1 = 2 and n2 = 3, 4, 5, ... Figure 7.11 The Bohr explanation of the three series of spectral lines. Figure B7.1 Flame tests strontium 38Sr Figure B7.2 copper 29Cu Emission and absorption spectra of sodium atoms. Bright Line Spectra of Several Elements 7.3 En = -RH ( En = -RH ( Z2 n2 1 n2 ) ) n (principal quantum number) = 1,2,3,… Z = Atomic Number (Hydrogen, Z = 1) RH = 2.18 x 10-18J Sample Problem 7.3 A hydrogen atom absorbs a photon of visible light and its electron transitions from the n = 1 to n = 4 energy level. Calculate (a) The change of energy of the atom, and (b) The wavelength (in nm) of the photon Figure B7.3 The main components of a typical spectrophotometer Lenses/slits/collimaters narrow and align beam. Source produces radiation in region of interest. Must be stable and reproducible. In most cases, the source emits many wavelengths. Sample in compartment absorbs characteristic amount of each incoming wavelength. Monochromator (wavelength selector) disperses incoming radiation into continuum of component wavelengths that are scanned or individually selected. Computer converts signal into displayed data. Detector converts transmitted radiation into amplified electrical signal. Louis De Broglie (1924) Q: Why is e- energy quantized? 1802 - T. Young 1905 - A. Einstein 1899 – J.J. Thomson - Light is a wave - Light is also a particle - e- is a particle - Maybe e- is also a wave!!! only certain frequencies can work in a circle with a particular radius l = h/mu Wave-like Properties Particle-like Properties u = velocity of em = mass of e- Sample Problem 7.4 Find the deBroglie wavelength of an electron with a speed of 1.00x106m/s (electron mass = 9.11x10-31kg; h = 6.626x10-34 kg*m2/s). l = h /mu Table 7.1 The de Broglie Wavelengths of Several Objects Substance Mass (g) Speed (m/s) l (m) slow electron 9x10-28 fast electron 9x10-28 5.9x106 1x10-10 alpha particle 6.6x10-24 1.5x107 7x10-15 one-gram mass 1.0 0.01 7x10-29 baseball 142 25.0 2x10-34 6.0x1027 3.0x104 4x10-63 Earth 1.0 7x10-4 G.P. Thomson (1925) The e- is also a wave! Exhibits properties similar to those of x-rays Thomson’s diffraction apparatus Figure 7.15 CLASSICAL THEORY Matter particulate, massive Energy continuous, wavelike Summary of the major observations and theories leading from classical theory to quantum theory. Since matter is discontinuous and particulate perhaps energy is discontinuous and particulate. Observation blackbody radiation Theory Planck: photoelectric effect Energy is quantized; only certain values allowed Einstein: Light has particulate behavior (photons) atomic line spectra Bohr: Energy of atoms is quantized; photon emitted when electron changes orbit. Figure 7.15 continued Since energy is wavelike perhaps matter is wavelike Observation Davisson/Germer: electron diffraction by metal crystal Theory deBroglie: All matter travels in waves; energy of atom is quantized due to wave motion of electrons Since matter has mass perhaps energy has mass Observation Compton: photon wavelength increases (momentumdecreases) after colliding with electron Theory Einstein/deBroglie: Mass and energy are equivalent; particles have wavelength and photons have momentum. QUANTUM THEORY Energy same as Matter particulate, massive, wavelike Heisenberg Uncertainty Principle Werner Heisenberg, 1926 Investigates limitations in pinpointing the position of an e- DxDp > h/4p AP Chemistry DxmDu > h/4p Bohr, Heisenberg, and Pauli POSITION of the e- is determined, "The more precisely the _____________ the less precisely the _________________ MOMENTUM is known" Uncertainty Principle A photon of “light” strikes an electron and is reflected (left). In the collision the photon transfers momentum to the electron. The reflected photon is seen through the microscope, but the electron is out of focus (right). Its exact position cannot be determined. Erwin Schroedinger (1926) Once at the end of a colloquium I heard Debye saying something like: Attempts to incorporate statistics with DeBroglie’s and Heisenberg’s work “Schroedinger, you are not working right now on very important problems… why don’t you tell us some time about that thesis of de Broglie’s… In one of the next colloquia, Schroedinger gave a beautifully clear account of how de Broglie associated a wave with a particle, and how he could obtain the quantization rules… When he had finished, Debye casually remarked that he thought this way of talking was rather childish… To deal properly with waves, one had to have a wave equation. Felix Bloch, Address to the American Physical Society, 1976 In the span of about two weeks, Schroedinger develops his wave equation ( x, t ) ( x, t ) V ( x, t ) ( x, t ) = ih 2 2m x t 2 2 “ epoch-making work” M. Planck “true genius” A. Einstein Schroedinger visits the University of Wisconsin, Madison to deliver a series of lectures in January and February 1927, introducing his his work on wave mechanics to American physicists and chemists : “Wave Function” 2: -A region in space in which there is a 90% chance of finding an electron ORBITAL -Also called an _______________ The Schrödinger Equation H = E wave function d2 dx2 + d2 dy2 mass of electron + d2 dz2 how changes in space potential energy at x,y,z 8p2mQ + (E-V(x,y,z)(x,y,z) = 0 2 h total quantized energy of the atomic system Figure 7.16 Electron probability in the ground-state H atom Where 90% of the e- density is found for the 1s orbital e- density (1s orbital) falls off rapidly as distance from nucleus increases “Anyone who is not shocked by quantum theory does not understand it” --Niels Bohr, 1897 “No one understands quantum theory” --Richard Feynman, 1967 Schrodinger Wave Equation = fn(n, l, ml, ms) Existence (and energy) of electron in atom is described by its unique wave function . No two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (Camp Randall, E, R12, S8) Each seat can hold only one individual at a time Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers. n the principal quantum number - a positive integer l the angular momentum quantum number - an integer from 0 to n-1 ml the magnetic moment quantum number - an integer from -l to +l Principal Quantum Number (Shell) = fn(n, l, ml, ms) principal quantum number = n n = 1, 2, 3, 4, …. distance of e- from the nucleus n=1 n=2 n=3 Figure 7.17 1s 2s 3s Angular Momentum Quantum Number (Subshell) = fn(n, l, ml, ms) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 l=0 l=1 l=2 l=3 s orbital p orbital d orbital f orbital Shape of the “volume” of space that the e- occupies l=0 l=1 l=2 l=3 s orbital p orbital d orbital f orbital Figure 7.18 The 2p orbitals Figure 7.15 A Cross Section of the Electron Probability Distribution for a 3p Orbital Figure 7.19 The 3d orbitals Figure 7.19 continued Figure 7.20 One of the seven possible 4f orbitals Magnetic Quantum Number = fn(n, l, ml, ms) magnetic quantum number ml for a given value of l ml = -l, …., 0, …. +l if l = 1 (p orbital), ml = -1, 0, or 1 if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2 orientation of the orbital in space Quantum Numbers and Atomic Orbitals An atomic orbital is specified by three quantum numbers. n the principal quantum number - a positive integer l the angular momentum quantum number - an integer from 0 to n-1 ml the magnetic moment quantum number - an integer from -l to +l Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Quantum Numbers Principal, n Positive integer (size, energy) (1, 2, 3, ...) 1 Angular momentum, l 0 to n-1 (shape) 0 0 0 0 Magnetic, ml -l,…,0,…,+l (orientation) 2 3 1 0 1 2 0 -1 0 +1 -1 0 +1 -2 -1 0 +1 +2 Sample Problem 7.5 Determining Quantum Numbers for an Energy Level PROBLEM: What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3? PLAN: Follow the rules for allowable quantum numbers found in the text. l values can be integers from 0 to n-1; ml can be integers from -l through 0 to + l. SOLUTION: For n = 3, l = 0, 1, 2 For l = 0 ml = 0 For l = 1 ml = -1, 0, or +1 For l = 2 ml = -2, -1, 0, +1, or +2 There are 9 ml values and therefore 9 orbitals with n = 3. Sample Problem 7.6 Determining Sublevel Names and Orbital Quantum Numbers PROBLEM: Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 PLAN: Combine the n value and l designation to name the sublevel. Knowing l, we can find ml and the number of orbitals. SOLUTION: n l sublevel name possible ml values # of orbitals (a) 3 2 3d -2, -1, 0, 1, 2 5 (b) 2 0 2s 0 1 (c) 5 1 5p -1, 0, 1 3 (d) 4 3 4f -3, -2, -1, 0, 1, 2, 3 7 Sample Problem 7.6 Determining Sublevel Names and Orbital Quantum Numbers PROBLEM: Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 PLAN: Combine the n value and l designation to name the sublevel. Knowing l, we can find ml and the number of orbitals. SOLUTION: n l sublevel name possible ml values # of orbitals (a) 3 2 3d -2, -1, 0, 1, 2 3 (b) 2 0 2s 0 1 (c) 5 1 5p -1, 0, 1 3 (d) 4 3 4f -3, -2, -1, 0, 1, 2, 3 7 Sample Problem 7.8: Identifying Incorrect Quantum Numbers What is wrong with each of the following quantum number designations and/or sublevel names? n l ml Name a) 1 1 0 b) 4 3 +1 4d c) 3 1 -2 1p 3p Energy of orbitals in a multi-electron atom Energy depends on n and l n=3 l = 2 n=3 l = 0 n=2 l = 0 n=1 l = 0 n=3 l = 1 n=2 l = 1 Writing Orbital Diagrams and Electron Configurations Aufbau Principle: Electrons fill from lowest to highest energy levels Hund’s Rule: Each orbital must half fill before it completely fills Pauli Exclusion Principle: No 2 e-s can have the same quantum numbers Each orbital can hold 2 electrons with opposite spin NOT Practice: Write Electron Configurations for: 1s22s22p63s23p1 [Ne]3s23p1 [He]2s22p6 OR Al 22s22p6 1s OR 3+ Al 24p5 22s22p63s23p64s23d104p5 [Ar]4s 1s OR Br 2 6 Br- 1s22s22p63s23p64s23d104p6 OR [Ar]4s 4p [Ar]4s13d5 Cr Cu [Ar]4s13d10 Why does 4s fill before 3d? Cu1+ [Ar]3d10 Zn2+ [Ar]3d10 Outermost subshell being filled with electrons Terms – Isoelectronic: • Atoms/Ions that have the same electron configurations – Core electrons: • Electrons in the lower energy levels – Valence electrons: • Electrons in the outer energy level Quantum Numbers A series of numbers that describe the properties of an orbital The “address of an electron” Spin Quantum Number = fn(n, l, ml, ms) spin quantum number ms ms = +½ or -½ ms = +½ ms = -½ 7.6 Para/Diamagnetism • Paramagnetism attracted to a magnetic field unpaired electrons • Diamagnetism repelled by a magnetic field paired electrons Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p 7.8 Determining Para/Diamagnetism Substance is placed between electromagnets. If the substance appears heavier, it is attracted in the magnetic field, and is paramagnetic. If the substance appears lighter, it is diamagnetic. Magnet Video These links need to be fixed Nitrogen Video Oxygen Video Write electron configuration for each and predict para- or dia-magnetic Na+ Para or Dia? 1s22s22p6 Dia 1s22s22p63s23p6 Dia 1s22s22p63s23p6 Dia 1s22s22p63s23p63d10 Dia 1s22s22p63s23p63d9 Para 1s22s22p63s23p63d5 Para 1s22s22p63s23p63d3 Para 1s22s22p63s23p6 Dia NaCl ClCaSO4 Ca2+ ZnSO4 Zn2+ CuSO4 Cu2+ MnSO4 Mn2+ MnO2 KMnO4 +4 ? Mn ? Mn+7