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Unformatted text preview: Chapter 39: MORE ABOUT MATTER WAVES 1. If a wave function for a particle moving along the x axis is normalized, then: A. $   2 dt = 1 B. $   2 dx = 1 C. / x = 1 D. / t = 1 E.   2 = 1 ans: B 2. The energy of a particle in a onedimensional trap with zero potential energy in the interior and in f nite potential energy at the walls is proportional to ( n = quantum number): A. n B. 1 /n C. 1 /n 2 D. n E. n 2 ans: E 3. The ground state energy of an electron in a onedimensional trap with zero potential energy in the interior and in f nite potential energy at the walls is 2 . 0 eV. If the width of the well is doubled, the ground state energy will be: A. 0 . 5 eV B. 1 . 0 eV C. 2 . 0 eV D. 4 . 0 eV E. 8 . 0 eV ans: A 4. An electron is in a onedimensional trap with zero potential energy in the interior and in f nite potential energy at the walls. The ratio E 3 /E 1 of the energy for n = 3 to that for n = 1 is: A. 1 / 3 B. 1 / 9 C. 3 / 1 D. 9 / 1 E. 1 / 1 ans: D 586 Chapter 39: MORE ABOUT MATTER WAVES 5. A particle is trapped in a onedimensional well with in f nite potential energy at the walls. Three possible pairs of energy levels are 1. n = 3 and n = 1 2. n = 3 and n = 2 3. n = 4 and n = 3 Order these pairs according to the di f erence in energy, least to greatest. A. 1, 2, 3 B. 3, 2, 1 C. 2, 3, 1 D. 1, 3, 2 E. 3, 1, 2 ans: C 6. Identical particles are trapped in onedimensional wells with in f nite potential energy at the walls. The widths L of the traps and the quantum numbers n of the particles are 1. L = 2 L , n = 2 2. L = 2 L , n = 4 3. L = 3 L , n = 3 4. L = 4 L , n = 2 Rank them according to the kinetic energies of the particles, least to greatest. A. 1, 2, 3, 4 B. 4, 3, 2, 1 C. 1 and 3 tied, then 2, 4 D. 4, 2, then 1 and 3 tied E. 1, 3, then 2 and 4 tied ans: D 7. Four di f erent particles are trapped in onedimensional wells with in f nite potential energy at their walls. The masses of the particles and the width of the wells are 1. mass = 4 m , width = 2 L 2. mass = 2 m , width = 2 L 3. mass = 4 m , width = L 4. mass = m , width = 2 L Rank them according to the kinetic energies of the particles when they are in their ground states. A. 1, 2, 3, 4 B. 1, 2, 3 and 4 tied C. 1 and 2 tied, then 3, 4 D. 4, 3, 2, 1 E. 3, 1, 2, 4 ans: B Chapter 39: MORE ABOUT MATTER WAVES 587 8. The ground state energy of an electron in a onedimensional trap with zero potential energy in the interior and in f nite potential energy at the walls: A. is zero B. decreases with temperature C. increases with temperature D. is independent of temperature E. oscillates with time ans: D 9. An electron is in a onedimensional trap with zero potential energy in the interior and in f nite potential energy at the walls. A graph of its wave function ( x ) versus x is shown. The value of quantum number n is: x ....
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 Spring '08
 Halstead
 Energy

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