Ch40Word - Chapter 40 p. 1 CHAPTER 40 – Quantum Mechanics...

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Unformatted text preview: Chapter 40 p. 1 CHAPTER 40 – Quantum Mechanics of Atoms Note: At the atomic scale, it is most convenient to have energies in electron-volts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its wavelength is E = hf = hc / λ = (6.63 × 10 –34 J ∙ s)(3 × 10 8 m/s)(10 9 nm/m)/(1.60 × 10 –19 J/eV) λ ; E = (1.24 × 10 3 eV ∙ nm)/ λ . 1. The value of ¬ can range from 0 to n – 1. Thus for n = 6, we have ¬ = 0, 1, 2, 3, 4, 5 . 2. The value of m ¬ can range from – ¬ to + ¬ . Thus for ¬ = 3, we have m ¬ = – 3, – 2, – 1, 0, 1, 2, 3 . The possible values of m s are – ! , + ! . 3. The value of ¬ can range from 0 to n – 1. Thus for n = 4, we have ¬ = 0, 1, 2, 3. For each ¬ the value of m ¬ can range from – ¬ to + ¬ , or 2 ¬ + 1 values. For each of these there are two values of m s . Thus the total number for each ¬ is 2(2 ¬ + 1). The number of states is N = 2(0 + 1) + 2(2 + 1) + 2(4 + 1) + 2(6 + 1) = 32 states . We start with ¬ = 0, and list the quantum numbers in the order ( n , ¬ , m ¬ , m s ); (4, 0, 0, – ! ), (4, 0, 0, + ! ), (4, 1, –1, – ! ), (4, 1, –1, + ! ), (4, 1, 0, – ! ), (4, 1, 0, + ! ), (4, 1, 1, – ! ), (4, 1, 1, + ! ), (4, 2, – 2, – ! ), (4, 2, – 2, + ! ), (4, 2, –1, – ! ), (4, 2, –1, + ! ), (4, 2, 0, – ! ), (4, 2, 0, + ! ), (4, 2, 1, – ! ), (4, 2, 1, + ! ), (4, 2, 2, – ! ), (4, 2, 2, + ! ), (4, 3, – 3, – ! ), (4, 3, – 3, + ! ), (4, 3, – 2, – ! ), (4, 3, – 2, + ! ), (4, 3, – 1, – ! ), (4, 3, – 1, + ! ), (4, 3, 0, – ! ), (4, 3, 0, + ! ), (4, 3, 1, – ! ), (4, 3, 1, + ! ), (4, 3, 2, – ! ), (4, 3, 2, + ! ), (4, 3, 3, – ! ), (4, 3, 3, + ! ). 4. The value of m ¬ can range from – ¬ to + ¬ , so we have ¬ = 3 . The value of ¬ can range from 0 to n – 1. Thus we have n = ¬ + 1 (minimum 4). There are two values of m s : m s = – ! , + ! . 5. The value of ¬ can range from 0 to n – 1. Thus for ¬ = 4, we have n = 5 ....
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This homework help was uploaded on 03/26/2008 for the course PHYS 208 taught by Professor Ross during the Spring '08 term at Texas A&M.

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Ch40Word - Chapter 40 p. 1 CHAPTER 40 – Quantum Mechanics...

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