Chp 6: Atomic Structure

Transcription

1 Chp 6: Atomic Structure 1. Electromagnetic Radiation 2. Light Energy 3. Line Spectra & the Bohr Model 4. Electron & Wave-Particle Duality 5. Quantum Chemistry & Wave Mechanics 6. Atomic Orbitals

2 Overview Chemical Reactions are a Result of Electron Interactions Between Various Elements Elemental Behavior Is the Result of the Element s Electronic Structure Periodic Table is Based on an Elements Electronic Structure

3 How Do We Study an Elements Electronic Structure Through the Interaction of Light and Matter How Does Matter Interact with Light?

4 1. Absorption - An Electron Absorbs the Light, Acquiring It s Energy and Entering an Excited State 2. Emission - An Electron Relaxes to a Lower Energy State While Emitting Light Name Some Characteristics of Light

5 1. Light Travels Through Space 2. Light has Color 3. Light has Energy 4. Light Energy is Quantized So What Is Light?

6 6.1 Electromagnetic Radiation Wavelength (l) - Distance Between two Peaks Frequency (u) - How Often Waves Goes Through a Complete Cycle (1/sec = hertz) Speed (c) - How Fast Wave Propagates c = 3 X 10 8 m/sec c=lu

7 Spectrum l c u u c l

8 6.2 Nature of Matter: Wave- Particle Duality Light exhibits both wave and particle behavior. Photon - Particle of Light E = nhn, where n = # of photons (Einstein) Einstein s Photoelectric Effect

9 Electromagnetic Radiation & Energy Planks Constant relates the Energy of a photon of light to it s frequency. E=hu h=planck s Constant h= 6.63X10-34 J. sec How do we relate the Energy of light to it s wavelength? from c lu E h c l

10 Electromagnetic Radiation & Energy Small Wavelength High Frequency High Energy Large Wavelength Low Frequency Low Energy E=hu Wavelength (meters)

11 Light Intensity I = nhu (n = moles of photons) Think about the video on Einstein s photoelectric effect and the difference between intense red light and weak blue light

12 Photon Energy Problem How many photons of microwave radiation ( =125mm) are required to heat 1 L of water from 20.0 o C to the boiling point? n hc n ms( Tf Ti) l msl( Tf Ti) n hc g J 0 l 6.626x10 J sec 3x10 o 0 1l m (100 C 20 c) g C E Light = q nhu = msdt 34 8 m sec 29 mol n 2.10x kmol x10 -Use s for specific heat capacity as c is the speed of light

13 6.3 Atomic Line Spectra Light Emitted or Absorbed by Atoms Occurs at Specific Energies or Colors

14 Sodium Line Spectra Sodium gives off yellow light of a specific wavelength of nm. What is the frequency of the yellow line spectra of sodium? u c ln c u l x nm m s m 9 10 nm x10 / sec

15 Sodium Line Spectra Sodium gives off yellow light of a specific wavelength of nm. 1. Determine E for a photon of sodium yellow light c E hn h l x10 m s E x J s 3.37x10 J m nm 9 10 nm 2. Determine E for a mole of photons of sodium yellow light c E nhn nh l E x photons x KJ mol J photon 203 /

16 Bohr Model of Hydrogen Atom Correctly Described the Hydrogen Spectrum Used Concept of Orbits (Wrong) Used Concept of Quantized Energy Levels (Right)

17 Bohr Equation for Hydrogen Energy of the nth level: R H = Rydberg constant R H =Rhc E n R H 1 ( 2 n ) R H = 2.18x10-18 J Energy for transition n i --> n f : 1 1 DEn ( ) i n E f n E f n hu R i h n n 2 2 f i DE hu n i n f R 1 n 1 n h( 2 2 i f )

18 Bohr Model of Hydrogen Atom n f = 1 for UV light n f = 2 for visible light n f = 3 for IR light

19 Bohr Problem: What Is the Energy Level of the Excited State Which Is Responsible for the Blue Green Emission Line at nm? That is, what is the initial quantum state; n i? Emission is an exothermic process Absorption is an endothermic process DE electron E photon n hc 1 1 photon l electron H n n E h E R ( ) 2 2 i f

20 Bohr Problem: h n hc l R H 1 1 n i n f ( 2 2 ) hc lr H 1 1 ( 2 2 n f ni ) n i 1 n 2 f 1 lr hc H (6.63x10 34 Js )(3x10 8 m / s) (486.1 x10 9 m )(2.18x10 18 J ) n i = 4

21 7.4 Wave-Particle Duality De Broglie s Hypothesis: All Matter has a Characteristic Wavelength 2 hc E mc hv l l h mv v=velocity & mv = momentum Note the inverse relationship between the mass and the wavelength c v

22 mv = h l mc = h l DeBroglie Wavelength of Electron Calculate the DeBroglie Wavelength of an Electron moving at 1.00% the speed of light c = 3x10 8 m/s, m=9.11x10-31 kg E = mc 2 E = hu c=lu mc 2 = hu u c l mc 2 = hc l

23 DeBroglie Wavelength of Electron Calculate the DeBroglie Wavelength of an Electron moving at 1.00% the speed of light c = 3x10 8 m/s, m=9.11x10-31 kg h mv l 34 h 6.636x10 J s l mv x kg x m s 24nm

24 Wave-Particle Duality Electron Diffraction l elec = 2.4 x m and is diffracted by a crystal like NaCl

25 Wave-Particle Duality - Uncertainty The characteristic wavelength of an electron in a hydrogen atom is 240pm The size of an isolated H atom is about 240 pm This leads to an uncertainty in the location of the electron

26 Heisenberg s Uncertainty Principle You can not simultaneously know both the position and momentum of an electron To measure the position of an electron, you need a wavelength smaller than it s characteristic wavelength, which is of such a high energy that it alters the electron s position during the measurement process

27 Physical Meanings of Wave Functions Bohr Model Uses Orbits Quantum Mechanics Uses Orbitals (Y 2 ) Y 2 - Probability Distribution Function, Describes the probability of finding an electron in a specific location for a given energy state

28 Physical Meanings of Wave Functions Bohr Model Uses Orbits Quantum Mechanics Uses Orbitals (Y 2 ) Orbitals are Probability Distribution Functions - They Represent the Probability of Finding an Electron at a Certain Space in Time Different Orbitals Are Defined by Their Shapes and Distance From the Nucleus

29 Quantum Numbers Bohr Orbits Can Be Described by One Quantum Number, N, the Principle Quantum Number Quantum Mechanics Uses 4 Quantum Numbers n - Principle Quantum Number l - Azimuthal Quantum Number m l - Magnetic Quantum Number m s - Spin Quantum Number (Dirac)

30 Quantum Numbers Each Orbital Can Be Described by It s Set of Quantum Numbers No Two Electrons Can Have the Same Set of Quantum Numbers

31 n - Principle Quantum Number n has integral values; n = 1,2,3... n correlates to the shells and the periods of the periodic table There are n 2 orbitals in each shell The Larger the Value of n, the Greater the Average Distance From the Nucleus & the Greater the Orbital s Energy

32 l - Azmuthal Quantum Number Describes the shape of the orbital Use letters to designate values of l s: l=0 p: l=1 d: l=2 f: l=3 l has values of 0 to n-1 for each principle level -The 1st Principle Level has l = 0 - the 2nd has l = 0,1 - the 3rd has l = 0,1,2 - the 4th has l = 0,1,2,3 - all the rest have 4 or less 1s 2s, 2p 3s, 3p, 3d 4s, 4p, 4d, 4f

33 m l - Magnetic Quantum Number Describes Orientation in Space There are 2l+1 values of m l for each type of azmuthal quantum number with values ranging form l to -l 1 type of s (l = 0) orbital 3 types of p (l = 1) orbitals 5 types of d (l = 2) orbitals 7 types of f (l=3) orbitals

34 Each Orbital can be identified by it s Quantum numbers n Example, 2p x l, use letters s,p,d & f m l, describes orientation

35 6.6 Orbital Shapes & Energies: S Orbitals (l=0) Spherical in Nature Balloon Diagram shows region of 90% probability of finding electron All Periods Have S Orbitals 1s 2s 3s Onion Skin layers of 1st 3 S orbitals

36 s orbital radial probability functions Y 2 1s Y 2 2s Y 2 3s node nodes r r r

37 P Orbitals (l=1) There are 3 types of P orbitals 2 nd Period & Greater Have P Orbitals

38 d Orbitals (l=2) 5 types of d orbitals 3 rd Period & Greater Have d Orbitals

39 f orbitals 7 types of f orbitals 4 th Period & Greater Have f Orbitals