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Lecture Notes for Ch 7 The Quantum Mechanical Model of the Atom...

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

SUMMARY: Electromagnetic Spectrum

PRACTICE: Place the following types of electromagnetic radiation in order of decreasing energy: Ultraviolet light, Radio waves, Microwaves A. Radio waves > Microwaves > Ultraviolet light B. Ultraviolet light > Microwaves > Radio waves C. Radio waves > Ultraviolet light > Microwaves D. Ultraviolet light > Radio waves > Microwaves E. Microwaves > Radio waves > Ultraviolet light

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: What is the correct order of increasing energy? 1. microwaves, x-rays, γ-rays, visible light, ultraviolet light 2. microwaves, ultraviolet light, visible light, x-rays, γ-rays 3. ultraviolet light, visible light, microwaves, x-rays, γ-rays 4. x-rays, γ-rays, microwaves, visible light, ultraviolet light 5. microwaves, visible light, ultraviolet light, x-rays, γ-rays

PRACTICE: How much energy is contained in 1 mol of each of the following? a. X-ray photons with a wavelength of 0.135 nm. Express the energy numerically in kilojoules per mole. b. γ-ray photons with a wavelength of 2.38×10 −5 nm. Express the energy numerically in kilojoules per mole.

PRACTICE: Calculate the frequency of each of the following wavelengths of electromagnetic radiation. a. 488.0 nm (wavelength of argon laser)

b. 503 nm (wavelength of maximum solar radiation)

c. 0.0520 nm (a wavelength contained in medical X-rays)

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Green light has a frequency of about 6.00 x 1014 s-1 . What is the energy of a photon of green light? (4 sig. fig) E=J

PRACTICE: What is the wavelength (m) of light that has a frequency of 1.20 x 1013 s-1 a) 2.50 x 10-5 b) 25.0 c) 0.0400 d) 4.00 x 104 e) 2.5

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: One type of ultraviolet light has a wavelength of 223 nm. Calculate the energy of one photon of this light. a. 8.91 x 10 -19 J b. 6.95 x 10 -19 J c. 7.12 x 10 -19 J d. 7. 87 x 10 -19 J

PRACTICE: Calculate the wavelength (in nm) of the blue light emitted by a mercury lamp with a frequency of 6.88 ×1014 Hz. A) 229 nm B) 206 nm C) 436 nm D) 675 nm E) 485 nm

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Under which conditions is constructive interference observed at a point on the target screen in a two slit experiment with waves?

a. When waves from each slit arrive in-phase. b. When waves from each slit arrive 90° out of phase. c. When waves from each slit do not arrive at the point. d. When waves from each slit arrive at different times. e. Constructive interference is never observed.

SUMMARY: Photoelectric Effect

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: The first ionization energy of carbon is 1.81 aJ. Assuming an ionization efficiency of 22.35%, how many photons of the lowest possible frequency are required to ionize a sample of carbon that contains 5.32 x 1018 atoms? a) 2.38 x 1019 photons b) 4.20 x 10-20 photons c) 2.73 x 1015 photons d) 9.11 x 106 photons

PRACTICE: In an experiment of the photoelectric effect, an incident beam of ultraviolet radiation shined on a piece of metal and produced electrons with zero kinetic energy. Which of the following radiation would be most likely to produce electrons with some kinetic energy? A. radio wave B. microwave C. green light D. infrared E. gamma ray

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: The photoelectric effect provided evidence for the (wave, particle)-like behavior of light. The phenomenon of diffraction provided evidence for the (wave, particle)-like bahavior of light. 1. wave, wave 2. wave, particle 3. particle, wave 4. particle, particle

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: The figure below shows Ek plotted as a function of v for photoelectric emission from two metals, A and B. Which of the following statements for the two metals is correct? A. Both metals will produce the approximately equal currents under identical conditions. B. The threshold frequencies suggest that metal A is an alkali metal. C. The threshold frequency is the same for both metals. D. The threshold frequency of A is greater than that of B. E. The threshold frequency of A is less than that of B.

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: The mass of a golf ball is 45.9 g. If it leaves the tee with a speed of 69.0m/s, what is its corresponding wavelength? Express your answer numerically in meters.

PRACTICE: The mass of an electron is 9.11x10 -31 kg . If the de Broglie wavelength for an electron in a hydrogen atom is 3.31x10-10 m , how fast is the electron moving relative to the speed of light? The speed of light is 3.00 x 108 m/s . Express your answer numerically as a percentage of the speed of light.

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: In a scanning electron microscope (SEM), electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 1.7 x 104 meters per second. The mass of an electron is 9.1 x 10-28 g? a) 4.3 x 10 -11 m b) 4.3 x 10 -8 m c) 1.8 x 10 4 m d) 2.3 x 10 -35 m e) 2 x 10 -33 m PRACTICE: As the velocity of an object doubles, what is expected of its deBroglie wavelength of the object? A. It will increase by a factor of four B. It will increase by a factor of two C. It will remain constant D. It will decrease by a factor of two E. It will decrease by a factor of four

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 103 m/s, the uncertainty in its position (in m) is at least (mass electron = 9.11 x 10 31 kg) __.

A) 1.7 x 10-8 m B) 6.6 x 10-8 m C) 17 m D) 66 m E) None of these choices is correct

PRACTICE: To what uncertainty (in m) can the position of a baseball traveling at 45.0 m/s be measured if the uncertainty of its speed is 0.10%? The mass of a baseball is about 0.145 kg. a. 8.1 x 10-33 m b. 5.6 x 10-15 m c. 6.7 x 10-45 m d. 5.9 x 10-14 m e. 4.4 x 10-65 m

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

PRACTICE: Which electron transition produces light of the highest frequency in the hydrogen atom? a. 2p → 1s b. 4p → 1s c. 3p → 1s d. 5p → 1s PRACTICE: Which electronic transition in atomic hydrogen corresponds to the emission of visible light? a) n = 5 → n = 2 b) n = 1 → n = 2 c) n = 3 → n = 4 d) n = 3 → n = 1

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Which of the following statements is or are true? 1. An excited atom can return to a lower energy level by absorbing light energy. 2. An atom can be excited by emitting light energy. 3. As the energy of electromagnetic radiation increases, its frequency increases. 4. The frequency and wavelength of light are inversely proportional. a) 1 and 2 only b) 2 only c) 2 and 3 d) 1 and 3 e) 3 and 4

PRACTICE: How many unique emission lines are observed from a system with four equally spaced energy levels? a. 1 b. 2 c. 3 d. 4 e. 5

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

SUMMARY: Bohr and Balmer Equations

PRACTICE: How much energy is required to ionize hydrogen: a. When it is in the ground state and

b. When it is in the 2nd excited state with n = 3.

PRACTICE: An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Calculate the wavelength of light associated with the transition from n=1 to n=3 in the hydrogen atom. A. 103 nm B. 155 nm C. 646 nm D. 971 nm E. 136 nm

PRACTICE: How many nodal planes are present in a 3f orbital? 1. 5 2. 4 3. 7 4. 2 5. 3

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: The graph shows the radial distribution plots for the 1s wavefunction for H, He, and He+. Which plot is the 1s wavefunction for the He + ion? 1. A 2. B 3. There is no way to know 4. C

SUMMARY: Introduction to Quantum Mechanics

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: a. For n=4, what are the possible values of l?

b. For l=2, what are the possible values of ml?

c. If ml is 2, what are the possible values for l?

PRACTICE: What are the possible values of n and m l for an electron in a 5d orbital? a) n = 1,2,3,4, or 5 and m l = 1 b) n = 1,2,3,4 or 5 and m l = -2, -1, 0, +1, or +2 c) n = 4 and m l = -1, 0, or l d) n = 5 and m l = 2 e) n = 5 and m l = -2, -1, 0, +1 or +2

PRACTICE: Give the number of possible orbitals in an H atom with the values: n = 3 l, l = 1 a. 1 b. 2 c. 3 d. 4 e. an infinite number

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: What is the lowest numbered principal energy level in which d orbitals are found? A. 1 B. 2 C. 3 D. 4 E. 5

PRACTICE: Which of the following sets of quantum numbers is not allowed? a) n = 3, l = 1, m l = +1 b) n = 3, l = 0, m l = 0 c) n = 4, l = 2, m l = +2 d) n = 4, l = 1, m l = 0 e) n = 4, l = 2, m l = +3

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Which of the following set of quantum numbers (ordered n, ℓ, m ℓ, ms ) are possible for an electron in an atom? Check all that apply. a. 5, 3, 0, 1/2 b. 2, 1, 0, 1/2 c. 3, 1, 0, -1/2 d. 2, 1, 0, 1 e. 2, 1, -2, 1/2 f. 3, 4, 0, 1/2 g. 5, 3, 4, 1/2 h. -1, 0, 0, -1/2

PRACTICE: Which of the following is a possible set of quantum numbers?

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: What is the smallest acceptable value for the missing quantum number? n = ?, ℓ = 2, mℓ = 0, ms = +1/2 A) 4 B) 3 C) 1 D) 5 E) 2

SUMMARY: Orbital Shapes

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: All of the following statements are true, EXCEPT: a. the n = 2 energy level has d orbitals b. the 2p orbitals can have a max of 6 electrons c. the s orbital has a spherical shape d. there are 5 d orbitals in a set e. the fourth major energy level has one set of f orbitals.

PRACTICE: Use the relative size of the 3s orbital represented below to answer the following question. In an atom, how many other orbitals will have both a value of n and a shape identical to Orbital C? (Use Orbital C as a reference and do not include it in your count.) a. 1 b. 2 c. 3 d. 4

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Which sketch represents an orbital with the quantum numbers n = 3, l = 0, and ml = 0?

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: Which of the following statements is TRUE?

a. Atoms are roughly spherical because when all of the different shaped orbitals are overlapped, they take on a spherical shape. b. We can know the exact location and exact speed of an electron at the same time. c. Since electrons have mass, we must always consider them to have particle properties and never wavelike properties. d. All orbitals in a given atom are roughly the same size. e. All of the above are true.

PRACTICE: Which quantum numbers below could correctly describe the orbital to the right? (a) n = 1, l = 0, m l = 0 (b) n = 2, l = 2, m l = 1 (c) n = 3, l = 1, m l = -1 (d) n = 3, l = 2, m l = -3 (e) n = 3, l = 2, ml = 2

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CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM*

PRACTICE: In a one-dimensional particle in a box, for n = 6, how many wavelengths equals the size of the box? 1.) 1 2.) 2.5 3.) 6 4.) 3 5.) 12

PRACTICE: In a one-dimensional particle in a box, for Ψ 4 , how many nodes are predicted? 1. 1 2. 4 3. 2 4. 3 5. 0

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