HW5.2 - nguyen (jn9225) – H05: Atomic Theory – mccord...

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Unformatted text preview: nguyen (jn9225) – H05: Atomic Theory – mccord – (50950) 1 This print-out should have 33 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The work function for chrominum metal is 4.37 eV. What wavelength of radiation must be used to eject electrons with a velocity of 4800 km / s? Correct answer: 17 . 7574 nm. Explanation: v = 4800 km / s = 4 . 8 × 10 6 m / s The wavelength of radiation needed will be the sum of the energy of the work function plus the kinetic energy of the ejected elctron. E work function = (4 . 37 eV) × (1 . 6022 × 10- 19 J / eV) = 7 . 00161 × 10- 19 J E kinetic = 1 2 m v 2 = 1 2 (9 . 10939 × 10- 31 kg) × (4 . 8 × 10 6 m / s) 2 = 1 . 0494 × 10- 17 J E total = E work function + E kinetic = 7 . 00161 × 10- 19 J + 1 . 0494 × 10- 17 J = 1 . 11942 × 10- 17 J Since c = ν λ , E = h ν = h c λ λ = h c E = 6 . 626 × 10- 34 m 2 · kg / s 1 . 11942 × 10- 17 J × 3 . × 10 8 m / s = 1 . 77574 × 10- 8 m × 10 9 nm 1 m = 17 . 7574 nm 002 10.0 points Which of the following provided evidence that the electrons in atoms are arranged in distinct energy levels? 1. the deflection of ions in a mass spectrom- eter 2. the results of the Millikan oil-drop exper- iment 3. the existence of elements with noninteger values for atomic weights 4. the scattering of α particles by a metal foil 5. the observation of line spectra from gas discharge tubes correct Explanation: The fact that gases emitted only specific wavelengths of energy suggested that electron energy states are quantized. 003 10.0 points Assume n 1 and n 2 are two adjacent energy levels of an atom. The emission of radiation with the longest wavelength would occur for which two values of n 1 and n 2 ? 1. 6,5 2. 2,1 3. 7,6 4. 5,4 5. 8,7 correct 6. 3,2 7. 4,3 Explanation: The frequency of a photon emitted when an electron moves between levels n 1 and n 2 is given by the Rydberg equation: ν = R parenleftbigg 1 n 2 1- 1 n 2 2 parenrightbigg , nguyen (jn9225) – H05: Atomic Theory – mccord – (50950) 2 where R = 3 . 29 × 10 15 Hz. The emission of radiation with the longest wavelength corre- sponds to that with the smallest frequency. From inspection of the formula above we see that ν is smallest when n 1 = 8 and n 2 = 7. Conceptual Solution : E = h ν = h R parenleftbigg 1 n 2 1- 1 n 2 2 parenrightbigg gives the energy of the pho- tons emitted. The emission of radiation with the longest wavelength corresponds to pho- tons with the smallest energy. From the Bohr frequency condition the energy of the emit- ted photon must be equal to the difference in energy between the higher and lower lev- els. An energy level diagram for the H-atom shows that as the energy levels get higher, the gaps between them converge; of the transi- tions listed, the two adjacent levels which are the closest together are n 1 = 8 and n 2 = 7....
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This note was uploaded on 10/01/2011 for the course CHEM 301 taught by Professor Wandelt during the Fall '08 term at University of Texas.

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HW5.2 - nguyen (jn9225) – H05: Atomic Theory – mccord...

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