Kami Export - PS10-Orbitals Quantum

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Brigham Young University *

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105

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Chemistry

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Jan 9, 2024

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Orbitals Quantum 1. Louis deBroglie correctly postulated that matter has wavelike properties. According to the Guinness Book of World Records, the fastest baseball pitch by a man was thrown by the Cuban pitcher Aroldis Chapman in 2010. What was the deBroglie wavelength of the baseball (0.145 kg) he threw at 105.1 mph (46.98 m/s)? 2. A synchrotron is a type of particle accelerator in which a ring of variable electric and magnetic fields accelerates particles (electrons, protons, etc.) to speeds nearing the speed of light. The largest synchrotron in the world is the Large Hadron Collider in Geneva, Switzerland where protons ( m p = 1.6726x10 -27 kg) can be accelerated to speeds of 0.999999991 c . (a) What is the de Broglie wavelength of one of these protons? (b) What is the wavelength of an electron (m e = 9.109x10 –31 kg) moving at that same speed? (not considering relativistic effects) 3. (a) What do wave functions ( Ψ ) tell you? (b) What are quantum numbers and how are they related to the wave function? (c) What does the square of the wave function ( Ψ 2 ) tell you? (d) What is an orbital? 4. What is the difference between the orbit as described by the Bohr model, and the orbital as described by the quantum theory?

5. For each of the 4 types of quantum numbers give the name of the quantum number, its letter/symbol, the range of its possible values, and explain in 1-3 sentences what property is related to each quantum number. 6. (a) What are the possible values of quantum number l when n = 3? (b) Which are the possible values of m l when l = 3? 7. (a) What is a node? (b) How many total nodes will any given orbital have? (c) What is the difference between a planar and a radial node? (d) How can you tell how many planar and radial nodes an orbital will have? (e) For the n=3 shell, how many total nodes will each orbital have? How many nodes are radial and how many are planar?

8. Which subshell corresponds to each of the following sets of quantum numbers? a. n = 3, l = 2 b. n = 4, l = 0 9. (a) Which of the following sets of quantum numbers ( n, l, m l , m s ) are actually possible? If a set of quantum numbers is impossible, explain why. a. 3, 2, -2, ½ b. 1, 1, 0, ½ c. 1, 0, 1, -½ d. 0, 0, 0, ½ e. 2, 0, 3, -½ 10. Identify the number of planar nodes, radial nodes, and the total number of nodes in the following orbitals. From that information, label each orbital with the appropriate shell and subshell values.

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