Principles 1 Week 9

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Tuesday March 12, 2024 Day 36 Light and its Wave Nature
Textbook Readings 7.1: Schrödinger's Cat 7.2: The Nature of Light OS: 3.1 Electromagnetic Energy	Course Lectures 7.1 pdf Video* Light and Waves 7.2 pdf Video* Light and Energy 7.3 pdf Video* Light Waves and Calculations
Electromagnetic Radiation	Frequency, Wavelength, and the Speed of Light
Objectives 1. Describe an electromagnetic light wave and identify its wavelength, amplitude and frequency. 2. Describe what's known as the electromagnetic spectrum and label its parts. 3. Describe how energy, wavelength and frequency change within the electromagnetic spectrum 4. Give examples of frequency in daily life and how it changes. 5. Use the relationship c = λ ν to determine wavelength or frequency for light where c = 3.00 x 10⁸ m/s ...the speed of light 6. Use the relationship E = hv to determine the energy of light with specific frequency. 7. Describe what's meant by wave-particle duality for light (i.e. what's a photon?)	Wave-Particle Duality and the Photoelectric Effect
Homework Problems 37.1 Identify the labeled parts of the electromagnetic wave below. 37.2 Identify and know the parts of the electromagnetic spectrum below 37.3 A laser emits light of frequency 4.74 x 10¹⁴ sec-1. Use c = λ ν to determine the wavelength of the light in nm. 37.4 An electromagnetic light wave has a wavelength of 625 nm. a. What is the frequency of the wave? b. What region of the electromagnetic spectrum is it found? c. What is the energy of the wave? 37.5 Use "c", the speed of light to determine how many minutes would it take a radio wave to travel from the planet Venus to the Earth. (Average Venus to Earth distance is 28 million miles) 37.6 Microwave ovens emit microwave energy with a wavelength of 12.9 cm. What is the energy of exactly one photon of this microwave radiation? (Source) 37.7 In photoelectric effect experiments, no photoelectrons are produced when the frequency of the incident radiation drops below a cutoff value regardless of how bright or intense the light is. How is this explained using a “particle” theory of light instead of a wave theory of light? 37.8 Photoelectric Effect: With a particular metal plate, shining a beam of green light on the metal causes electrons to be emitted. a. If we replace the green light by blue light, will electrons be emitted? b. If we replace the green light by red light, will electrons be emitted? Click and drag below for answers: 1. a. wavelength b. amplitude (height) c. trough d. trough e. crest 2. a. visible spectrum b.high frequency c. low frequency d. gamma rays e. x-rays f. ultraviolet light g. infrared (radiant heat) h. microwaves i. radio waves j. short wavelengths k. long wavelengths l. light energy increases right to left. 3. 6.32 x 10² nm 4. a. 4.80 x 10¹⁴ s^-1 b. Visible (400 - 750 nm) c. 3.18 x 10 ^-19 J 5. 2.5 minutes 6. E= 1.54 x 10^-24J 7.. When the frequency of light hitting a surface is lower than a cut-off value (threshold frequency), photons will not have enough energy to release electrons from the surface. This is because energy of a photon is directly proportional to frequency of the light and not the amplitude of the wave ...also known as brightness or intensity intensity. 8.. a. Yes. Since blue light has greater energy than green light, there is more than enough energy to remove an electron via the photoelectric effect. b. Maybe. Red light has lower energy than green light. If the bare minimum energy required to eject an electron was provided by green light, then red light will have no effect. However, if the threshold light energy is lower than what red light provides, then electrons will still be ejected from the metal surface.

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Wednesday March 13, 2024 Day 37 Spectroscopy and the Bohr Atom
Textbook Readings 7.3: Atomic Spectroscopy and The Bohr Models	Course Lectures 7.5 pdf Video* Spectroscopy and the Rydberg Equation 7.7 pdf Video* Stationary States and Electron Transitions
Bohr Model of the Hydrogen Atom	Spectroscopy and Stationary States
Objectives 1. Describe Bohr's model of the atom. 2. Describe how the "n" value relates to spaces (rings or orbits) within a simple atom. 3. Compare electrons with different "n" values in terms of their potential energy. 4. Describe what happens to an atom's electron location and energy when light energy is absorbed or emitted. 5. Describe what is meant by an electron transition. 6. Describe the differences between a line spectrum and a continuous spectrum. 7. Explain why regions of "blackness" are observed between lines in a line spectrum. 8. Calculate the energy of an electron before and after a transition. Calculate ΔE for an electron transition and use it to calculate the frequency and wavelength of the light absorbed or released.
Homework Problems 38.1. In the Bohr model pictured below, determine the initial "n" value, the final "n" value and whether the electron transition is the result of light energy absorbtion or emission. 38.2. For each of the above transitions, use the Rydberg equation to determine the energies associated with both the initial and final states you determined in 38.1. 38.3. Use the calculated energies from question #2 to determine the electron's energy change for each transition. Remember, ΔE = E_final - E_initial. Be sure to include the negative sign as needed. 38.4. Use your results from #3 to determine the frequency and wavelength of the light emitted or absorbed by the atom. Use this information to identify the type of electromagnetic radiation using the electromagnetic spectrum. 38.5 The energy of the transition can be inferred from the length of the arrow drawn from "ni" value to to nf. In the diagram above, which arrow is the longest? Which arrow is the shortest? Compare to the ΔE values above. 38.5. In your own words why there are regions of "darkness" between the lines in a "line spectrum" 38.6. As you know, ionization and the formation of an anion is the complete removal of an electron from the atom. What is the energy required to completely remove an electron that's located initially in the n = 1 orbit? What type of electromagnetic radiation could accomplish this? Click and drag the region below for correct answers 38.1 a. n_i = 2 → n_f = 1 Light Energy Emission b. n_i = 2 → n_f = 4 Energy Absorpsion c. n_i = 3 → n_f = 5 Energy Absorpsion d. n_i = 5 → n_f = 1 Light Energy Emission 38.2 a. E₂ = -5.450 x 10^-19 J E₁ = -2.180 x 10^-18 J b. E₂ = -5.450 x 10^-19 J E₄ = -1.3625 x 10^-19 J c. E3 = -2.422 x 10^-19 J E₅ = -8.720 x 10^-20 J d. E₅ = -8.720 x 10^-20 J E₁ = -2.180 x 10^-18 J 38.3 a. ΔE = -1.635 x 10^-18J (negative tells us the atom has lost energy) b. ΔE = 4.088 x 10^-19 J (positive value tells us the atom has absorbed energy) c. ΔE = 1.550 x 10^-19 J d ΔE = -2.093 x 10^-18 J 38.4 a. v= 2.468 x 10¹⁵ s^-1 λ = 121.6 nm Ultraviolet Electtromagnetic Radiation b. v = 6.169 x 10¹⁴ s^-1 λ = 486.3 nm Blue visible Electtromagnetic Radiation c. v = 2.340 x 10¹⁴ s^-1 λ = 1282. nm Infrared Electtromagnetic Radiation d. v = 3.158 x 10¹⁵ s^-1 λ = 94.98 nm Ultraviolet Electtromagnetic Radiation 38.5 The n_i = 5 → n_f = 1 is the longest arrow and involves the largest energy change of those listed in 38.2. The n_i = 3 → n_f = 5 is the shortest arrow and involves the smallest energy change of those listed in 38.2. 38.6 There are no "levels" within the atom from which an electron can move from or go to that will produce light in the dark regions of the spectrum. The existance of lines in the line spectrum is proof of specific, quantized energy levels (orbits) within the atom and provide a unique fingerprint for each element. 38.7 Initially the electron has n_i= 1. If the electron is removed, n_f = ∞ (Infinity). ΔE for the atom = 2.18 x 10^-18 J ( v= 3.29 x 10¹⁵ s^-1 λ = 91.2 nm ... Ultraviolet EM radiation)

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Thursday March 14, 2024 Day 38 Particles are also Waves? Huh?
Textbook Readings 7.4: The Wavelength Nature of Matter	Course Lectures 7.4 pdf Video* Particles and Waves
The Double Slit Experiment	Matter as a Wave
Objectives 1. Give examples of both waves and particles 2. Know why the wave nature of every-day objects isn't observable. 3. Calculate the wavelength of paricles using the de Broglie relationship 4. State in words the meaning of the Heisenberg Uncertainty Principle. 5. Use the Heisenberg Uncertainty Principle mathematical relationship to calculate uncertainty in velocity and position.	The Heisenberg Uncertainty Principle Part 1
Homework Problems 40.1. State in your own words why wave-like behavior isn't observed for objects in our physical world. 40.2 Use the de Broglie relationship to determine the wavelength of a 150. gram baseball traveling at 90.0 mph. 40.3 How many times bigger is the length of a 1.0 meter baseball bat than the wavelength of the baseball calculated above? 40.4 What is the wavelength of a marble sized stone (m = 10.0 g) if it has a wavelength of 4.50 × 10^-33 m? 40.5 Consider again the baseball from problem #4. It has a mass of 150. g and travels at 90 mph. a. If the uncertainty in the baseball's velocity is +/- 2 mph, use the Heisenberg Uncertainty equation to determine the uncertainty in the baseball's position b. Is the baseball's position uncertainty enough to justify the batter missing the pitched ball? 40.6 Consider an electron with mass of 9.11 x 10 ^-31 kg traveling at 10,000. m/s +/- 1.00% a. What is the uncertainty in the electron's position? b. How does the position uncertainty compare to the diameter of an atom, approx. 1 x 10^-10m? c. What does this say about a moving electron in the atomic environment? Click and drag the region below for correct answers 40.1 The wavelength of everyday objects is real ... but very small in comparison to the dimensions of the surroundings. Until the wavelength of an object approaches the sizes of things in the 40.2 1.10 x 10^-34 m 40.3 The bat is 9 x 10³³ times larger than the wavelength of the baseball 40.4 14.7 m/s 40.5 a. Δx = 3.93 x 10^-34 m b. The result from "a" is so very small. The error in the ball's position is many, many, many factors of 10 smaller than anything in the physical world. The ball's position uncertainty will be of no consequence and if the batter misses the ball, it is her/his mistake (strike). 40.6 a. Δx = 5.79 x 10^-7 m. b. The uncertainty of the traveling electron is 1000 x larger than that of a typical atom and significant in this setting. c. We may know it's velocity, but we don't know much about where the electron is in relation to other nearby atoms.

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Friday March 15, 2024 Day 39 Quantum Mechanics and the Atom
Textbook Reading 7.5: Quantum Mechanics and The Atom	Course Lectures 7.8 pdf Video Schrodinger Equation and Atomic Quantum Numbers
Standing Waves and Harmonics	The Schrodinger Equation
Objectives 1. Describe traveling waves and how they form standing waves (e.g. on a rope). 2. Describe the connection between circular standing waves and the allowed orbits for electrons around the atom's nucleus. 3. Explain what new electron property the Schrodinger equation incorporates into quantum mechanics. 3. Provide the first three quantum numbers that describe electrons in an atom. 5. Construct or identify combinations of quantum numbers that do or do not follow the rules.	Quantum Numbers, Atomic Orbitals, and Electron Configurations (Through 2:40)
Homework Problems 41.1 View this video and describe how the instructor creates a "traveling wave" 41.2 Using the same video, explain what happens to a traveling wave when it hits the end of the rope. 41.3 What must the instructor do to create a standing wave? Draw pictures of the first 4 possible standing wave patterns for a rope.
41.4 Linear standing waves are created when two oppositely traveling waves interfere with each other (image at right). Identify the two traveling waves by travel direction and color. Identify the standing wave and its fixed "nodes" and oscillating "antinodes. "
41.5 Circular standing waves describe electrons in an atom because, as you know, electrons have wavelike behavior. The diagram at right illustrates one such electron standing wave (nucleus would be at the center). How many complete wavelengths can be identified in this picture?
41.6 The quantum numbers n, l and m_l describe electrons in atoms. What physical property does each quantum number relate to? 41.7 What are the rules that determine which quantum numbers are possible for electrons in an atom? 41.8 Examine the following sets of quantum numbers and identify them as correct or incorrect. If incorrect, identify the problem and fix it. a. n = 1 l = 2 m_l= 0 b. n = 3 l = 2 m_l= -1 c. n = 2 l = -2 m_l= 1 d. n = 2 l = 1 m_l= -1 e. n = 1 l = 0 m_l= 0 f. n = 3 l = 2 m_l= -3 g. n = 2 l = 2 m_l= +1 h. n = 2 l = 1 m_l= 0
Click and drag the region below for correct answers 41.1 The traveling wave is created by "jiggling" the rope at one end. 41.2 The traveling wave is reflected when it reaches the end of the rope. Also notice it is "inverted". 41.3 The instructor must continue "jiggling" the end of the rope to create left and right traveling waves that interfere with each other. 41.4. The blue traveling wave moves right. The red (reflected) traveling wave moves left. The black "standing wave" is the result of the two traveling waves interferring with eachother. The red dots identify the nodes (they appear fixed) and the up/down black peaks of maximum amplitude are antinodes. 41.5 For a standing wave, you must have 2 regions of high amplitude to equal one wavelength. In this case, there are 8 regions that fit perfectly into the circle. This corresponds to 4 wavelengths. 41.6 The "n" quantum number, known as the principle quantum number is an indication of the size of the space occupied (a.k.a. orbital) and the electron's PE. The "l" quantum number, known as the azimuthal quantum number, describes the shape of region of space occupied by the electrons (a.k.a. orbital). The m_l quantum number, known as the magnetic quantum number , describes the orientation or direction of the electrons spacial region (a.k.a. orbital) 41.7 The Principle Quantum Number n can have values from 1 all the way to infinity ∞ The Azimuthal Quantum number l can have values that depend on the "n" value: l = 0, 1, 2, .... up to a maximum of (n-1) The Magnetic Quantum Number can have values that depend on the "l" value: m_l = -l .... 0 .... +l 41.7 a. Incorrect l cannot be greater than n - 1. Corrected: n = 1 l = 0 m_l= 0 b. Correct c. Incorrect l cannot be negative and must be less than n - 1: Corrected: n = 2 l = +1 m_l= 1 d. Correct e. Correct f. Incorrect m_l must be in the range of -l ... 0 ... +l Corrected: n = 3 l = 2 m_l=0 g. Incorrect. l cannot be greater than n - 1. Corrected: n = 2 l = 1 m_l= +1 h. Correct.

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