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UT CH 301 - Study guide

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Fall 2007 CH301 Worksheet 2 Answer Key 1. A pool cue ball has a mass of 170 g. Assume that the position of the ball is known with an uncertainty of the width of a hydrogen atom, about 1.20 Å. What is the minimum uncertainty in its velocity? 2.58 x 10-34 m/s – or the width of a proton about every 12 years! 2. Repeat the calculation, but this time with an electron, which has a mass of 9.11 x 10-31 kg. Does the uncertainty in the velocity become significant? 482 km/s – over a million miles an hour! 3. What is the de Broglie wavelength for the cue ball moving at a leisurely speed of 1 m/s? 3.90 x 10-33 m – ridiculously small. 4. What is the de Broglie wavelength of an electron moving at the not-so-leisurely speed of 100 km/s? 7.27 nm – very large on the length scale of an electron in an atom 5. What is the de Broglie wavelength of a 70-kg person jogging at 2.5 m/s? 3.77 x 10-36 m 6. Stars can be treated as black-body radiators, so that their temperatures can be approximated from their spectra. The star Betelgeuse has a λmax = 800 nm. What is the temperature of Betelgeuse, in degrees Celsius? 3327 ºC 7. Given that Betelgeuse has a radius of 4.524 x 1011 m, how much power is emitted from Betelgeuse? 2.45 x 1031 W 8. What is the minimum temperature at which a black body can be for its λmax to be in the visible spectrum (400-700 nm)? 4114 K 9. Explain briefly, in your own words, what is meant by “the ultraviolet catastrophe.” Classical mechanics predicts that a black body should emit radiation with infinite power – specifically, as the wavelength of radiation decreases, the power with which it is emitted should increase to infinity. Obviously, this isn't what actually happens. 10. Which of the following sets of quantum numbers are valid of an electron? What is wrong with the ones that aren't? (a) n = 1 l = 1 ml = 0 ms = ½ (b) n = 3 l = 1 ml = -1 ms = -½ (c) n = 2 l = 0 ml = 0 ms = 1 (d) n = 5 l = 2 ml = -3 ms = ½(a) Invalid – l must be between 0 and n-1. (b) Valid. (c) Invalid – ms must be ±½. (d) Invalid – ml must be between -l and l. 11. Briefly explain the so-called “wave-particle duality.” All matter, as well as light, exhibits characteristics of a wave, such as diffraction, as well as characteristics of a particle, such as quantization. 12. A scientist shines lights at a metal, but does not detect the release of any electrons. In classical theory, what should the scientist do to make some electrons be ejected? Crank up the power – classical theory predicts that electrons will be ejected more energetically if the metal is hit with higher-intensity light. 13. What should the scientist actually do to get electrons to be emitted? Use a higher-frequency light source, because the energy delivered to the electrons (thus, the energy with which they are released) is proportional to the frequency of the light. 14. Once electrons are being emitted, what effect will increasing the intensity of the light have? More electrons will be emitted, since the metal is hit with more photons. 15. What effect will increasing the frequency have? The velocity with which the electrons leave will increase, since more energy is imparted to each. 16. Calculate the energy of a photon with wavelength 550 nm. 3.61 x 10-19 J 17. What would be the wavelength of emission expected from the n = 4 to n = 2 transition for hydrogen? 485 nm 18. What happens to the energy difference between levels as n increases for the particle in a box? What about for the hydrogen atom? They increase for the PiaB, but decrease for the hydrogen atom. 19. Why isn't the probability density for the electron in the hydrogen atom highest at the nucleus? The radial distribution predicts that because the volume shrinks to zero as the radius does, the probability of finding the very near the center is very small. 20. List the wavelengths of the wave functions for the first 3 energy levels of a particle in a box of length L. λ1 = 2L, λ2 = L, λ3 = 2/3 L21. What is the ground-state electron configuration for chlorine? 1s22s22p62s22p5 = [Ne]2s22p5 22. How many electrons go into each s orbital for n = 1 to 4? Each p orbital? In both cases, 2. 23. How many electrons can go into the n = 2 shell of an atom? The n = 3 shell? n = 2: 8; n = 3: 18 24. List the following orbitals in order of increasing energy in the hydrogen atom: 3s, 2p, 5s, 3d, 4p, 4s 2p < 3s < 4s < 3d < 4p < 5s 25. The Pauli exclusion principle states that no two electrons can have the same set of quantum numbers. What is the practical consequence of this when assigning electrons to orbitals? No more than two electrons can be in any single orbital. 26. What effect does shielding have on the energy of electrons in outer shells of a many-electron atom? Electrons between the outer shell and the nucleus partly counteract the effect of the nucleus, increasing the energy. 27. An atom has 4 electrons in its 2p subshell. In the boxes below, draw their configuration, using arrows to indicate the spins of the electrons. ↑ ↓ ↑ ↑ 28. How many electrons can go into the 3d subshell of an atom? 10 electrons 29. What is the ground state electron configuration of tungsten, W? 1s22s22p63s23p64s23d104p65s24d105p66s24f145d4 = [Xe]6s24f145d4 30. What is the meaning of “degenerate” with regard to atomic orbitals? Degenerate orbitals are orbitals of the same energy.31. How many unpaired electrons are in the ground state of sulfur? 2 32. How many unpaired electrons are in the ground state of arsenic, As? 3 33. What is the ground-state electron configuration of Fe3+? 1s22s22p63s23p64s23d3 = [Ar]4s23d3 34. An electron is located in a state with n = 5, l = 1,and ml = 0. In what type of orbital is the electron located? 5p 35. What would be the wavelength of emission expected from the n = 5 to n = 1 transition for hydrogen? 94.7 nm 36. How many radial nodes are present in a 2s orbital? 1 37. How many electrons can go into the 2p subshell of an atom? 6 38. Give the principle and angular quantum numbers for (a) a 3d orbital and (b) a 4f orbital. (a) n = 3; l = 2 (b) n = 4; l = 3 39. What physical characteristic of the orbital does l correspond to? What about ml? l = the shape of the orbit, ml = the


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UT CH 301 - Study guide

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