Chap 6A - Chem 210 Chapter 6 A / WANG Waves Characteristics...

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Unformatted text preview: Chem 210 Chapter 6 A / WANG Waves Characteristics Characteristics Chapter 6.1 through 6.3 Electronic Electronic Structure of Atoms 1. Up-and-Down motion Up-and• Frequency or wavelength • Amplitude or intensity 6.1 Wave Nature of Light 6.2 Quantized Energy and Photons 6.3 Bohr’s Atomic Model / intro to Quantum Mechanical Atomic Model Online practice goal: achieve >90% in Chap 6. goal: homework 5 and Quiz 5 EOC (end-of-chapter problems) (end-of6.14, 6.16, 6.36, 6.44, 6.54, 6.64, 6.68, 6.74 (textbook page 253-255) 253- due due date – Wed. Sept. 23rd 2. Forward motion • Speed or velocity Wave Nature of Light Maxwell proposed(1873) : light consists of light electromagnetic waves called: waves, electromagnetic radiation. Up-andUp-and-down motion composed of 2 waves composed perpendicular to each other: – Electric field + Magnetic field Magnetic • Forward motion in a in vacuum vacuum moves at the speed speed of light: • c = 3.00 x 108 m/sec 3.00 sinclair/diff.html Wave Characteristics of electromagnetic electromagnetic radiation How do we know electromagnetic radiation is composed of waves? • Electromagnetic radiation shows diffraction diffraction patterns characteristic of all waves. characteristic waves. – Two sets of water waves running into each other will show patterns of destructive and destructive and constructive interferences. constructive interferences. – Same as rays of light shining through two tiny holes next to each other. – We detect common objects by the patterns patterns of visible light diffraction along the edges of diffraction along these objects. • Fall 2009 UM-SJTU JI • Electromagnetic radiation includes infra red (IR), includes ultraviolet (UV), x ray, microwave, gamma ray….. and visible light. visible • Different types of electromagnetic radiation have electromagnetic different different wavelengths, but they all move through ll a vacuum at the same speed vacuum speed 3.00 3.00 x 108 m/sec Pictures on the left show typical diffraction patterns of water waves going through slit(s). Note the diffraction patterns. Thomas Young's sketch of two-slit twodiffraction, which he presented to the Royal Society in 1803 Page 1 Chem 210 Chapter 6 A / WANG Diffraction pattern caused by light passing light through two adjacent slits. Wave Characteristics of electromagnetic electromagnetic radiation Further explanation on “electromagnetic waves”. • Wave characteristics of electromagnetic radiation come from the periodic oscillations of periodic of its electric and magnetic components. electric and magnetic components. – The strengths of electric and magnetic fields strengths fields rise-andrise-and-ebb like water waves. Different behaviors of waves and particles. Wave Characteristics of electromagnetic electromagnetic radiation Or, Or, c = λν Speed of light = wavelength x frequency frequency c=λν Speed = length / time (m⋅s-1) Frequency = 1/ time (s-1) Wavelength = length (m, µm, nm, etc.) Higher frequency ↔ Shorter wavelength Fall 2009 UM-SJTU JI Amplitude (intensity) of a wave is a separate property. It is independent of wavelength or frequency. Page 2 Chem 210 Chapter 6 A / WANG Wavelength (λ) Range of Visible light λ around 0.4 µm to 0.7 µm = 400 to 700 nm (1µm = 1000 nm) (1 = 4000 to 7000 A (1 nm = 10 A) (1 Frequency (ν) Range of Visible light Definition of ν, frequency: frequency: number The number of complete waves (cycles) that passes through a given point in one second. one Unit: Cycle per second = sec-1 = Hertz (Hz) sec Hertz Visible wavelength range is 400nm – 700 nm. • at λ = 400 nm ν=c/λ (3.00 ν = (3.00 x 108 m sec-1) ÷ (400 x 10-9 m) sec ν = 7.50 x 1014 sec-1 Hz ν = 7.50 x 1014 Hz • at λ = 700 nm ν = 4.29 x 1014 Hz Visible light frequency range: 4.29 x 1014 Hz to 7.5x1014 Hz Observation: Coal at 1000 K Coal 1000 appears red. Filament at Filament 2000 2000 K appears white. smoldering coal red hot light bulb filament – white hot Max Planck explained that “red hot” object releases releases mostly lower ν of visible + lower Infra red radiation of lower lower energy temperature energy / temperature; “white” hot object releases wider w ider range and higher and frequencies at higher higher temperature / energy. energy. Fall 2009 UM-SJTU JI Frequency ν ↔wavelength λ Question: National Public Radio in the U.S. is heard at FM 91.1. What is the wavelength of this radio wave? Hint: FM 91.1 means: 91.1 MHz = 91.1 x 106 cycles per second Answer: λ=? λ=c/ν = (3.00 x 108 m sec-1) ÷ (91.1 x 106 sec-1) = 3.29 m The wavelength of this radio wave is 3.29 m. Max Planck’s “Quantum” Max Planck related energy to frequency, and first used the term quantum in 1900 quantum to denote “the smallest quantity of quantity energy that can be emitted or absorbed by atoms as electromagnetic radiation.” electromagnetic He proposed that energy (E) of a quantum is proportional to its frequency: its E = h ⋅ν He was awarded the 1918 Nobel Prize in Planck’s constant physics for this work on h = 6.63 x 10-34 J-s. 6.63 the Quantum theory. Quantum theory. Page 3 Chem 210 Chapter 6 A / WANG Einstein’s “Photon” experimental evidence of quantum theory Einstein Einstein applied (1905) Planck’s quantum theory quantum to explain the photoelectric photoelectric effect and received the 1921 Nobel Prize in physics for this interpretation (NOT for the relativity theory!). • PAGE 222 TEXT TEXT • Quick Time movie photo_ef photo_ef. ParticleParticle-Waves Duality: Is light a Is wave or a particle? • Light has wave characteristics – diffraction patterns of electromagnetic radiation. Energy of “photon” or “quantum” E = hν Find the energy of a quantum of x ray with ν = 3 x 1018 s-1. How much energy is in 1 mole of this type of photons? Further Observation of light Spectrum continuous spectrum – Produced by the sun • Light also has particle characteristics photoelectric effect and the quantum theory. • Particle-wave duality is established Particlewith respect to light: Line Spectrum – Produced from atoms (gas) of discharge tubes – It’s both a w ave and a particle! Sun Sun light or light from heated solids or appears white, which separates into which a continuous spectrum. Fall 2009 UM-SJTU JI Light emitted from heated gases in sodium gases or neon lamps or discharge tubes separates into a Line Spectrum, Line unique to each element! Page 4 Chem 210 Chapter 6 A / WANG The line spectra of several elements versus sun light. strontium 38Sr copper 29Cu Sun light mercury strontium Line spectra and Fireworks Emission spectrum of sodium atoms. hydrogen Bohr’s interpretation of the line spectrum Bohr’s Atomic Model • • In 1914, Niels Bohr published his explanation of Niels the Hydrogen line spectrum in relation to the electronic structure of the atom, and received the 1922 Nobel prize in physics for this work. Bohr’s The basic assumptions of Bohr’s atomic model: 1. Electrons move in circular orbits around the nucleus (planetary model) 2. Only orbits of certain radii, corresponding to specific allowed energy states are permitted. An atom normally is in the ground state. All electrons are arranged in lowest possible energy levels in the atom, one of which is shown here. 0 E ground level excited level E* E0 excited level Light! ground level Bohr’s Atomic Model Bohr’s Model explained explained the hydrogen spectral lines observed by Balmer (1885) in the visible region as resulting from electrons jumping from n = 5 2, 4 2, 2, 2, 3 2. 2. Fall 2009 UM-SJTU JI When energy is supplied by a flame or in an electrical discharge tube, the electron jumps to a higher energy level. The atom is now in an excited state, which is not very stable. The electron will not stay in the higher energy levels very long. The excited electron returns back to the original energy level by releasing the amount of energy that is equal to the difference between the two levels: E* - E0 = light. Emitting energy (E*-E0) to produce a spectral line in the line spectrum. The atom itself returns to the original ground state. Bohr’s model also explained other known series of spectral lines in the emission spectrum of the Hydrogen atom. Page 5 Chem 210 Chapter 6 A / WANG A quantum staircase showing how an electron can move up (absorbs energy) or down (emits energy) between energy levels in Bohr’s atom. Bohr’s equation for calculating electron energy in the Hydrogen atom Bohr’s Atomic Model Bohr’s Model succeeded in: 1. The idea of “only quantized energy states are quantized permitted.” 2. Explained the Hydrogen line spectrum: Hydrogen – Heating “excites” the electron to larger orbits. emitted – Light of specific wavelength is emitted when the electron returns from the higher energy orbit (excited state) back to a lower energy orbit (ground state). Calculate spectral line between ni & nf by Bohr’s equation ni 1 Ef = - RH ( nf ) 2 nf Ei = - RH ( 1 ) ni 2 RH = 2.18×10-18 J (Rydberg’s constant) (Rydberg’s n is called the “principal quantum number”. • The first orbit has n = 1, is closest to the first closest nucleus, and has negative energy by convention. E1 = - 2.18×10-18 J • The furthest orbit has n close to infinity furthest and corresponds to zero energy. E∞ = 0. Question: Calculate the wavelength of light involved for an electron transition in the Hydrogen atom from n = 5 to n = 2. ν= ν= ∆E RH = h h 1 1 2 − 2 ni n f ∆E 2.18 × 10 −18 J 1 1 = − = −6.90 × 1014 ⋅ s −1 h 6.63 ×10−34 J ⋅ s 52 22 ∆E R H = ν= h h −7 = 4.33 ×10 m = 433nm Fall 2009 UM-SJTU JI 1 1 2 − 2 n nf i • When ni > nf, energy is emitted (negative value). emitted (negative • When nf > ni, energy is absorbed (positive absorbed (positive value). value) Fill in the blank: The electron transition in the Hydrogen atom from n = ? to n = 2 corresponds to this red line. red E = Enf- Eni = - h (c/λ) = - 6.63 x10-34 (3.00x108 / 656 x10-9) 656 -19 = -3.032×10 1 1 = -2.18×10-18 × (n 2 − n 2 ) f λ = c ν = 2.99 ×108 m / s ÷ 6.9 ×1014 s −1 Spectral line ∆E = E f − Ei = hν i 11 0.139 ~ 2 − 2 32 Answer: Answer: From n=3 to n=2! Page 6 Chem 210 Chapter 6 A / WANG Bohr’s Atomic Model Limitations of Bohr’s Model: Can only explain one-electron atoms or oneions. Such as H, He+1 or Li+2 Cannot explain the line spectrum of atoms with more than one electron. Such as: He, C, or Na+1 Bohr’s model fails to explain elements other as than hydrogen because electrons have, as light has, both particle and wave properties. Modern Concept of the Atom QM atomic model uses wave or quantum quantized mechanics (QM) to determine the quantized electron energy levels by considering electrons as “waves”, which provides the probability of finding an electron in certain orbitals regions around the nucleus, called orbitals. Electrons are: “particles in orbits” in Bohr’s model vs. Bohr’s “waves / orbitals” in QM model. The “s” orbital Electron probability in the ground-state H groundatom. Fall 2009 UM-SJTU JI Page 7 ...
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This note was uploaded on 07/30/2011 for the course CHEM 210 taught by Professor Zhang during the Spring '09 term at Shanghai Jiao Tong University.

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