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AP Notes Chapter 6 Atomic Structure Describe properties of electromagnetic radiation Light & relationship to atomic structure Wave-particle duality Basic ideas of quantum mechanics Quantum numbers & atomic structure Electromagnetic Spectrum Light Made up of electromagnetic radiation. Waves of electric and magnetic fields at right angles to each other. Parts of a wave Wavelength l Frequency (n) = number of cycles in one second Measured in hertz 1 hertz (hz) = 1 cycle/second EMR - Wave Nature c = ln where c = Speed of light l = wavelength n = frequency l cycles 1 n: sec Hertz (Hz) sec EMR - Particle Nature (Quantized) Planck: E = hn E = energy h = Planck’s constant = 6.626 x 10- 34 J. s n= frequency Reminder kg m 1J 1 2 s 2 Kinds of EM waves There are many different l and n Radio waves, microwaves, x rays and gamma rays are all examples. Light is only the part our eyes can detect. Gamma Rays Radio waves The speed of light in a vacuum is 2.998 x 108 m/s =c c = ln= wavelength x frequency What is the wavelength of light with a frequency 5.89 x 105 Hz? What is the frequency of blue light with a wavelength of 484 nm? In 1900(s) Matter and energy were seen as different from each other in fundamental ways. Matter was particles. Energy could come in waves, with any frequency. Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave. Energy is Quantized Planck found DE came in chunks with size hn DE = nhn or nhc/l where n is an integer. and h is Planck’s constant h = 6.626 x 10-34 J s these packets of hn are called quantum Einstein is next Said electromagnetic radiation is quantized in particles called photons. Each photon has energy = hn = hc/l Combine this with Einstein’s E = mc2 You get the apparent mass of a photon. m = h / (lc) Neils Bohr (1885 –1962) Bohr Model of the Hydrogen Atom Energy Bohr model of the atom In the Bohr model, electrons can only exist at specific energy levels (orbit). The Bohr Ring Atom n=4 n=3 n=2 n=1 Bohr Model of Atom Postulates - P1: e revolves around the nucleus in a circular orbit Bohr Model of Atom Postulates P2:Only orbits allowed are those with angular momentum of integral multiples of: h 2 Bohr Model of Atom Postulates P3: e- does not radiate energy in orbit, but gains energy to go to higher level allowed orbit & radiates energy when falling to lower orbit Photo Absorption and Emission The Bohr Model n is the energy level for each energy level the energy is Z is the nuclear charge, which is +1 for hydrogen. E = -2.178 x 10-18 J (Z2 / n2 ) n = 1 is called the ground state when the electron is removed, n = E=0 We are worried about the change When the electron moves from one energy level to another. DE = Efinal - Einitial DE = -2.178 x 10-18 J Z2 (1/ nf2 - 1/ ni2) 1 1 DE k 2 2 nf ni Rotating Object Balance Centrifugal Force = electrical attraction of positive nucleus and negative e Centrifugal Force = Electrostatic Attraction 2 2 mv e 2 r 0r where 0 1.112 10 2 e v 0mr 2 10 Definition Angular By P2: Momentum = mvr h mvr n 2 By rearrangement: nh v 2mr By rearrangement: nh v 2mr 2 2 nh 2 v 2 2 2 4 m r 2 2 2 e nh 2 2 2 0mr 4 m r n h 0 r 2 2 4 me 2 2 For H-atom [n = 1] r = 5.29 x 10 -11 m or 52.9 pm = 0.529 Angstoms In general, when n = orbit a0 = radius of H-atom for n = 1 & Z = atomic # 2 n a0 r Z e To keep in orbit, must balance kinetic energy and potential energy 1 E 2 n 1 E -k 2 n where k = Rydberg constant -18 k = 2.179 x 10 J For the transition of an e- from an initial energy level (Ei) to a final energy level (Ef), we can write D E E f Ei 1 1 DE k 2 k 2 n n f i 1 1 DE k 2 2 n n i f Examples Calculate the energy need to move an electron from its to the third energy level. Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. Calculate the energy released when an electron moves from n= 5 to n=3 in a He+1 ion When is it true? Only for hydrogen atoms and other monoelectronic species. Why the negative sign? To increase the energy of the electron you make it closer to the nucleus. the maximum energy an electron can have is zero, at an infinite distance. The Bohr Model Doesn’t work. Only works for hydrogen atoms. Electrons don’t move in circles. The quantization of energy is right, but not because they are circling like planets. Which is it? Is energy a wave like light, or a particle? Yes Concept is called the Wave-Particle duality. What about the other way, is matter a wave? Yes The Quantum Mechanical Model A totally new approach. De Broglie said matter could be like a wave. De Broglie said they were like standing waves. The vibrations of a stringed instrument. Matter as a wave Using the velocity v instead of the wavelength n we get. De Broglie’s equation l = h/mv Can calculate the wavelength of an object. Examples The laser light of a CD is 7.80 x 102 m. What is the frequency of this light? What is the energy of a photon of this light? What is the apparent mass of a photon of this light? What is the energy of a mole of these photons? What is the wavelength? Of an electron with a mass of 9.11 x 10-31 kg traveling at 1.0 x 107 m/s? Of a softball with a mass of 0.10 kg moving at 125 mi/hr? Diffraction Diffraction Grating splits light into its components of light of different frequencies or wavelengths. When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effect Because the waves interfere with each other. A wave moves toward a slit. Comes out as a curve with two holes with two holes Two Curves with two holes Two Curves Interfere with each other with two holes Two Curves Interfere with each other crests add up Several waves Several waves Several Curves Several Severalwaves waves Several Curves Interference Pattern Louis de Broglie (1892-1987) Electrons should be considered waves confined to the space around an atomic nucleus deBroglie “connected” the wave & particle natures of matter c ln c l n c ln E hn c l n ch l E c ln E hn E mc 2 c l n ch l E c c ln l n ch E hn l E h 2 E mc l mc deBroglie & Bohr consistent deBroglie started with h l mv But, for constructive interference of a body orbiting in a circle 2r nl nh then, 2r mv nh mvr 2 Which is Bohr Postulate #2 n=2 n=3 n=5 Schroedinger Equation h 2 2 2 V E 2 8 m x y z 2 2 2 2 Where: V = potential energy of electron E = total energy of electron = wave function of electron For electron in ground state of hydrogen atom: (as a 1st approximation) Ae r ao Where: r = distance electron from nucleus ao = Bohr radius A 1 a 3 O 1 2 3 2 1 0 node 1 node 2 2 2 node 2 3 nucleus r 52.9 pm 2 50 100 150 200 Distance from nucleus (pm) 2 100 200 300 400 500 600 Distance from nucleus (pm) Heisenberg Uncertainty Principle h Dx D mv 4 Electron Probability Space & Quantum Numbers Quantum #s or QN ___, ___, ___, ___ n ml ms Principal QN = n n = 1, 2, 3, . . . ==> size and energy of orbital ==> relative distance of ecloud from nucleus for H: 1 E k 2 n Principal QN = n for all other: 2 z E k 2 n where z = nuclear charge -18 k = +2.179 x 10 joule Angular Momentum QN = 0 , 1, 2, ... (n - 1) Shape of e- cloud corresponds/defines sub-level Angular Momentum QN = n 1 2 3 4 l 0 0,1 # sub 1 2 spectral s s, p Magnetic (orbital) QN = ml (m) m ... 0... l 0 ml 0 s-orbital s - orbital Magnetic (orbital) QN = ml (m) m ... 0... l 0 1 ml 0 -1,0,+1 s-orbital (3) p-orbitals py pz px px pz py (3) p - orbital px , py , p z Magnetic (orbital) QN = ml (m) m ... 0... l 0 1 2 ml 0 s-orbital -1,0,+1 (3) p-orbitals -2,-1,0,+1,+2 (5) d-orbitals (3) (1) dxy , dyz , dxz dx 2 y2 d - orbitals (1) dz 2 Spin QN = ms (s) 1 ms 2 - spin of e on own axis max e n=1 - n=1 s n=2 max e 2 - n=1 s n=2 s 2 p 6 n=3 max e 2 8 - n=1 s n=2 s 2 p 6 n=3 s 2 p 6 d 10 max e 2 8 18 - - n=1 s n=2 s 2 p 6 n=3 s 2 p 6 d 10 max e = 2n2 2 8 18 Pauli Exclusion Principle n l 1 1 2 2 2 2 2 2 2 2 0 0 0 0 1 1 1 1 1 1 ml 0 0 0 0 -1 -1 0 0 1 1 s +1/2 -1/2 +1/2 -1/2 +1/2 -1/2 +1/2 -1/2 +1/2 -1/2 Orbital 1S 2s 2p Pauli Exclusion Principle 2 e- in same atom can have the same set of four quantum numbers No Electron Probability Space & Quantum Numbers Quantum #s ___, ___, ___, ___ n ml ms Principal QN = n n = 1, 2, 3, . . . ==> size and energy of orbital ==> relative distance of ecloud from nucleus for H: 1 E k 2 n Principal QN = n for all other: 2 z E k 2 n where z = nuclear charge -18 k = +2.179 x 10 joule Angular Momentum QN = 0 , 1, 2, ... (n - 1) Shape of e- cloud corresponds/defines sub-level Angular Momentum QN = n 1 2 3 4 l 0 0,1 # sub 1 2 spectral s s, p Magnetic (orbital) QN = ml (m) m ... 0... l 0 ml 0 (1) s-orbital Magnetic (orbital) QN = ml (m) m ... 0... l 0 1 ml 0 -1,0,+1 (1) s-orbital (3) p-orbitals Magnetic (orbital) QN = ml (m) m ... 0... l 0 1 2 ml 0 (1) s-orbital -1,0,+1 (3) p-orbitals -2,-1,0,+1,+2 (5) d-orbitals Magnetic (orbital) QN = ml (m) m ... 0... l 0 1 2 3 ml 0 -1,0,+1 -2,-1,0,+1,+2 -3,-2,-1,0,+1,+2,+3 (1) s-orbital (3) p-orbitals (5) d-orbitals (7) f-orbitals