Chapter 7: Electrons in Atoms. Electromagnetic Radiation

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1 Chapter 7: Electrons in Atoms Dr. Chris Kozak Memorial University of Newfoundland, Canada 1 Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium. A wave transmits energy. 10 1

2 EM Radiation Low ν High ν 11 Frequency, Wavelength and Velocity Frequency (ν) in Hertz Hz or s -1. Wavelength (λ) in meters m. cm µm nm Å pm (10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m) Velocity (c) x 10 8 m s -1. c = λν λ = c/ν ν= c/λ 12 2

3 What is the frequency of light corresponding to blue light? λ = 473 nm. c = 2.998x10 8 m s -1. A. 1.58x10-15 s -1 B. 1.42x10-15 s -1 C. 6.33x10-14 s -1 D. 1.42x10-2 s -1 E. 1.42x10 2 s -1 F. 6.33x10 14 s -1 G. 1.42x10 15 s -1 H. 1.58x10 15 s -1 Electromagnetic Spectrum 14 3

4 Constructive and Destructive Interference 15 Refraction of Light 16 4

5 Atomic Spectra Hydrogen Helium Lithium Sodium Potassium 17 Atomic Spectra 18 5

6 Blackbody Radiation 3 phenomena confounded physicists at the turn of the 20 th century: 1) Atomic Spectra 2) Photoelectric effect 3) Blackbody radiation When a solid object is heated to 1000K, visible light is emitted. As T increases, intensity and wavelength change. Why? This is characteristic of blackbody radiation (a hypothetical body that absorbs and emits all frequencies of radiation). We see the colour and intensity of light increase in each of these increase K Embers in a fire 1500 K Stove heating element 2000 K 19 Light bulb filament Quantum Theory Blackbody Radiation: So, heated bodies emit light. In Blackbody Radiation, Intensity (I) is inversely proportional to wavelength (λ), or, it increases with increasing frequency (v). I proportional to 1/λ. Classical theory predicts continuous increase of intensity with frequency. However, in reality the intensity drops off after specific wavelengths. Max Planck, 1900: Energy, like matter, is discontinuous. ΔE = Δnhν E is energy, n is a positive integer, h = x J. s (Planck s constant) and ν is frequency in hertz (s -1 ) 20 6

7 What is the energy corresponding to blue light? λ = 473 nm h= x J s, c=2.998x10 8 m s -1. Δ E = h ν, ν = c / λ Enter your answer between 0 and 1000 kj mol -1 Rank Responses Other The Photoelectric Effect Light striking the surface of certain metals causes ejection of electrons Wave properties of light is unable to explain some observations ν > ν o threshold frequency (Light must have a minimum frequency or no current flows) ne - a I # of e - depends on intensity (Absence of Lag time. Current flow is immediate. The metal does not accumulate energy to eject the electron as predicted by wave theory) E k α ν kinetic energy depends on frequency (Wave theory says that amplitude, not frequency is responsible so any colour of light should be able to do this so long as it is bright enough. This can t be right!) 22 7

8 The Photoelectric Effect 23 The Bohr Atom Electrons move in circular orbits about the nucleus (like in classical physics) Fixed set of stationary states (allowed orbits) Governed by angular momentum: nh/2π, n=1, 2, 3. Energy packets (quanta) are absorbed or emitted when electrons change stationary states The integral values that are allowed are called quantum numbers The energy of an electron becomes increasingly negative the closer it gets to the nucleus according to E = -R H /n 2. R H is a constant Why is electron E a negative value? E = -R H n 2 R H = x J 24 8

9 Energy-Level Diagram ΔE = E f E i = 1 = R H ( ni 2 1 n f 2 -R H n f 2 -R H n i 2 ) = hν = hc/λ 25 Ionization Energy of Hydrogen 1 ΔE = R H ( ni 2 1 n f 2 ) = hν As n f goes to infinity for hydrogen starting in the ground state: 1 hν = R H ( ) = R ni 2 H This also works for hydrogen-like (1-electron) species such as He + and Li 2+ hν = -Z 2 RH Z is the nuclear charge (number of protons) 26 9

10 Great, but what do we really need to know? Calculate the energy, frequency and wavelength for any hydrogen atom transition Identify the wavelengths of the electromagnetic spectrum as being in the UV, visible or IR regions. You should be able to do Examples & 7.5 in Tro (and the practice examples) 27 Summary of Bohr s Atomic Theory Electrons are in motion around the nucleus (orbits) But, for circular orbits, electrons would possess angular momentum (acceleration) and therefore radiate energy! So, using Planck s quantum hypothesis, 1) Electrons move in fixed orbits around the nucleus 2) Fixed orbits (stationary states) mean properties of individual electrons will have unique values, for example, the angular momentum is quantized based on the orbit in which the electron resides. 3) Electrons only pass between allowed orbits. This means that fixed quanta of energy are involved. QUANTUM NUMBERS! 28 10

11 What is Bohr s Theory Good For? Approximations of the energy associated with transitions (movement) of electrons ONLY in ions with one electron! Can t explain: spectra of species with more than one electron effect of magnetic fields on emission spectra It is an uneasy mixture of classical and non-classical physics. Modern quantum theory replaced Bohr theory in Which of the following transi1ons emits a photon with the greatest wavelength? A. n=4 to n=2 B. n=2 to n=1 C. n=4 to n=3 11

12 Determine the energy of light emiaed by a hydrogen atom for the transi1on of an electron from n=3 to n=2. Input an answer in kj mol - 1. Rank Responses Other hap://snews.bnl.gov/popsci/atom1.jpg What is the energy of the photon emiaed associated when the electron in O 7+ undergoes a n=3 to n=2 transi1on Input an answer in kj mol - 1. Rank Responses Other hap:// Oxygen%20Spec%20sm.jpg 12

13 Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality Heisenberg s Uncertainty Principle 33 Fire Photon Torpedoes! Wave-Particle Duality. Einstein suggested particle-like properties of light could explain the photoelectric effect. But diffraction patterns suggest photons are wavelike. de Broglie, 1924 Small particles of matter may at times display wavelike properties. The concept of the photon! 34 13

14 de Broglie and Matter Waves E = mc 2 hν = mc 2 hν/c = mc = p p = h/λ Einstein s Relativity Equation Planck s Equation for Energy Rearrange to give momentum, p Momentum carried by a photon in relation to its wavelength! λ = h/p = h/mu The wavelength is related to the mass of the particle (particle property) If matter waves exist for small particles, then beams of particles should exhibit the characteristic properties of waves: diffraction. 35 X-Ray Diffraction Structure 1 Structure

15 The Uncertainty Principle Werner Heisenberg Δx Δp h 4π Δx is uncertainty in position Δp is uncertainty in momentum We cannot measure the exact position or exact momentum of a subatomic particle simultaneously WHY?! 37 Sample Problems 1. Some Diamonds appear yellow because they contain nitrogen compounds that absorb purple light with a frequency of 7.23 x Hz. Calculate the wavelength in nm of absorbed light. 2. Calculate the E of one photon of UV (λ = 1 x 10-8 m), visible (λ = 5 x 10-7 m) and IR (λ = 1 x 10-4 m) light. What do the answers indicate about the relationship between λ and E? 3. Calculate the Energy required to remove an electron from a hydrogen atom in its ground state. 4. Calculate the wavelength of the transition from n = 4 to n = 1 in Hydrogen (one of the Lyman series of transitions). 5. Calculate the de Broglie wavelengths of a 50 kg mass travelling at ¼ the speed of light and for a proton (m = x kg) travelling at this speed. What do these wavelengths say about the wave properties of matter in relation to their size? 38 15

16 Wave Mechanics Standing waves. Nodes do not undergo displacement. 2L λ =, n = 1, 2, 3 n 39 Wave Functions ψ, psi, the wave function. Should correspond to a standing wave within the boundary of the system being described. Particle in a box. ψ = 2 L nπ x sin L 40 16

17 Probability of Finding an Electron 41 Wave Functions for Hydrogen Schrödinger, 1927 Eψ = Hψ H (x,y,z) or H (r,θ,φ) ψ(r,θ,φ) = R(r) Y(θ,φ) R(r) is the radial wave function. Y(θ,φ) is the angular wave function

18 Principle Shells and Subshells Principle electronic shell, n = 1, 2, 3 Angular momentum quantum number, l = 0, 1, 2 (n-1) I = 0, s l = 1, p l = 2, d l = 3, f Magnetic quantum number, m l = - l -2, -1, 0, 1, 2 +l 43 Orbital Energies 44 18

19 9-8 Interpreting and Representing the Orbitals of the Hydrogen Atom. 45 s orbitals 46 19

20 p Orbitals 47 p Orbitals 48 20

21 d Orbitals 49 Electron Spin: A Fourth Quantum Number 50 21

22 Electronic Structure of the H atom We have 3 quantum numbers for H n = 1 l = 0 m l = 0 m s 1s orbital Only one type of orbital orientation/ symmetry Only one electron (can be either +1/2 or -1/2) Ground State Configuration: 1s 1 51 Which of the following best represents an orbital with principal and angular momentum quantum numbers 4 and 1, respec1vely? A. B. C. D. E. 22

23 Multi-electron Atoms Schrödinger equation was for only one e -. Electron-electron repulsion in multi-electron atoms. Assume they have Hydrogen-like orbitals (by approximation). 53 Electron Configurations Three Main Principles Aufbau process. Build up and minimize energy. Pauli exclusion principle. No two electrons can have all four quantum numbers alike. Hund s rule. Degenerate orbitals are occupied singly first and with parallel spins

24 Which of the following orbital designa1ons is impossible? A. n=2, l = 0, m l = 0 B. n=3, l = 0, m l = 0 C. n=3, l = 1, m l = 1 D. n=3, l = 2, m l = - 1 E. n=3, l = 3, m l = - 3 Which of the following sets of quantum numbers is NOT matched with the orbital designa1on. A. n=1, l = 0: a 1s orbital B. n=2, l = 0: a 2p orbital C. n=3, l = 0: a 3s orbital D. n=3, l = 1: a 3p orbital E. n=3, l = 2: a 3d orbital 24

25 Orbital Energies 57 How many electrons can have the following set of quantum numbers? Rank n = 3 Responses 6 Other Energy 5s 4s 3s 2s 4p 3p 2p 4p 4p 3p 3p 2p 2p 4d 4d 4d 4d 4d 3d 3d 3d 3d 3d 1s Multi-Electron Atom Atom 25

26 Orbital Filling for Atoms Only 59 Aufbau Process and Hund s Rule spdf notation: C (carbon) 1s 2 2s 2 2p 2 Expanded notation: 1s 2 2s 2 2p x1 p y

27 Filling p Orbitals (Electrons in Boxes) 61 Filling the d Orbitals 62 27

28 To which element does the following orbital filling diagram belong? A. C B. N C. Si D. P E. None of these. Which of the following is the condensed electron conﬁgura1on for chlorine? A. [Ne]3p7 B. [Ne]3s23p5 C. [Ne]3s23p6 D. [Ne]3s23d5 E. [Ne]3s23p33d2 Cl2(g) Cl2(l) 28

29 The electron configura1on for Ca is A. [Ar]3s 2 B. [Ar]3s4s C. [Ar]4s 2 D. [Ar]3s 4 E. [Ar]4p 2 The electron configura1on for Br is A. [Ar] 4s 2 3d 10 4p 5 B. [Ar] 4s 2 4d 10 4p 5 C. [Ar] 4s 2 5d 10 4p 5 D. [Ar] 5s 2 4d 10 5p 5 E. [Ar] 4s 2 5d 9 4p 6 29

30 The electron configura1on for Mo is A. [Kr] 4s 2 3d 4 B. [Kr] 4s 2 4p 4 C. [Kr] 5s 2 5d 4 D. [Kr] 5s 2 4d 4 E. [Kr] 5s 1 5d 5 The electron configura1on for Sn is A. [Kr] 4s 2 3d 10 5p 2 B. [Kr] 5s 2 4d 10 5p 2 C. [Kr] 5s 2 5d 10 5p 2 D. [Kr] 5s 2 4d 10 5p 2 E. [Kr] 5s 2 6d 5 5p 2 30

31 Which of the following represents an excited state electron configura1on? A. C A.. B.. B. N C.. D.. C. O E.. D. Si 2s 2s 2s 3s 2p 2p 2p 3p E. P 3s 3p 8-12 Electron Configurations and the Periodic Table 70 31

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