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Chapter 7 The Quantum-Mechanical Model of the Atom 135 Solution: 6.626 500 nm X m = 5.00 X 10²⁷ m; E = 5.00 10²⁷ = 3.9756 X J/photon 3.9756 photon X X 6.022 X mol 10²³ photons X kJ = 239 kJ/mol Check: The units of the answer (kJ/mol) are correct. The magnitude of the answer is reasonable for a wavelength in the visible region. (c) Given: = 150 nm Find: E for 1 mol photons Conceptual Plan: nm m 6.022 Solution: 6.626 1.50 nm X = X 10⁻⁷ m; = = 1.3252 10⁻¹⁸ J/photon 1.50 1.3252 photon X X 6.022 X mol 10²³ photons X = kJ/mol Check: The units of the answer (kJ/mol) are correct. The magnitude of the answer is reasonable for a wavelength in the ultraviolet region. Note: The energy increases from the IR to the visible to the UV as expected. The Wave Nature of Matter and the Uncertainty Principle 7.47 The interference pattern would be a series of light and dark lines. 7.49 Given: m = 9.109 X 10⁻³¹ kg, = 0.20 nm Find: Conceptual Plan: m, Solution: 6.626 X = 3.6 X 10⁶ m/s Check: The units of the answer (m/s) are correct. The magnitude of the answer is large, as would be expected for the speed of the electron. 7.51 Given: m = 9.109 X 10⁻³¹ kg; = 1.35 X 10⁵ m/s Find: 1 Conceptual Plan: m, Solution: 6.626 = 5.39 X 10⁻⁹ m = 5.39 nm Check: The units of the answer (m) are correct. The magnitude is reasonable because we are looking at an electron. Copyright © 2017 Pearson Education, Inc.