57. An electron and a proton, each initially at rest, are

1. (II) The neutrons in a parallel beam, each having kinetic energy :fceV. are directed through two slits 0.50 mm apart. How far apart will the interference peaks be on a screen 1.0 m away? [Hint: first find the wavelength of the neutron.]

2. (II) Bullets of mass 3.0g are fired in parallel paths with speeds of 220m/s through a hole 3.0 mm in diameter. How far from the hole must you be to detect a 1.0-cm-diameter spread in the beam of bullets?

3. (I) A proton is traveling with a speed of (6.560 0.012) x 10s m/s. With what maximum accuracy can its position be ascertained? [Hint. Ap = m Aw.]

4. (I) If an electron's position can be measured to an accuracy of 2.0 x 10_s m. how accurately can its speed be known?

5. (I) An electron remains in an excited state of an atom for typically 10-8s. What is the minimum uncertainty in the energy of the state (in eV)?

6. (I) The Z boson, discovered in 1985. is the mediator of the weak nuclear force, and it typically decays very quickly. Its average rest energy is 91.19GeV, but its short lifetime shows up as an intrinsic width of 2.5 GeV (rest energy uncertainty). What is the lifetime of this particle?

7. (II) What is the uncertainty in the mass of a muon (; = 105.7 MeV/c2), specified in eV/c2, given its lifetime of 2.20/xs? [Hint: A % A/A/.]

8. (II) A free neutron (m = 1.67 x 10-27 kg) has a mean life of 900 s. What is the uncertainty in its mass (in kg)?

9. (II) An electron and a 140-g baseball are each traveling 150 m/s measured to an accuracy of 0.055%. Calculate and compare the uncertainty in position of each.

10. (Ill) Estimate the lowest possible energy of a neutron contained in a typical nucleus of radius 1.0 X 10-,5m. [Hint: a particle can have an energy at least as large as its uncertainty.]

11. (Ill) Use the uncertainty principle to show that if an electron were present in the nucleus (r 10l5m), its kinetic energy (use relativity) would be hundreds of MeV. (Since such electron energies are not observed, we conclude that electrons are not present in the nucleus.) [Hint: a particle can have an energy at least as large as its uncertainty.]

12. (Ill) How accurately can the position of a 3.00-keV electron be measured assuming its energy is known to 1.00%?

13. (I) For n = 6, what values can / have?

14. (I) For n = 5, 1 = 3. what are the possible values of mt and m5?

15. (I) How many electrons can be in the n = 6. 1 = 3 subshcll?

16. (I) How many different states are possible for an electron whose principal quantum number is n = 4? Write down the quantum numbers for each state.

17. (I) List the quantum numbers for each electron in the ground state of (a) carbon (Z = 6). (b) magnesium (Z = 12).

18. (I) List the quantum numbers for each electron in the ground state of nitrogen (Z = 7).

19. (I) Suppose a certain hydrogen atom has / = 4. What are the possible values for n. mt, and ms?

20. (I) Calculate the magnitude of the angular momentum of an electron in the n = 4, 1 = 3 state of hydrogen.

21. (II) If a hydrogen atom has mt = -3. what are the possible values of n. /, and ms1

22. (II) Show that there can be 18 electrons in a "g" subshell.

23. (II) What is the full electron configuration in the ground state for elements with Z equal to (a) 27. (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

24. (II) What is the full electron configuration for (a) selenium (Se). (b) gold (Au). (c) radium (Ra)? [Hint: see the periodic table inside the back cover.)

25. (II) A hydrogen atom is in the 6s state. Determine (a) the principal quantum number. (b) the energy of the state, (c) the orbital angular momentum and its quantum number /. and (d) the possible values for the magnetic quantum number.

26. (II) Estimate the binding energy of the third electron in lithium using the Bohr theory. [Hint: this electron has n = 2 and sees" a net charge of approximately +le.] The measured value is 5.36 eV.

27. (II) Show that the total angular momentum is zero for a filled subshell.

* 28. (II) For each of the following atomic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being violated: (a) 4p > 3p: (b) 2p - Is; (c) 3d 2d: (d) 4d -> 3s; (e) 4s - 2p.

29. (II) An excited H atom is in a 6d state, (a) Name all the states (/i, /) to which the atom is allowed to jump with the emission of a photon. (b) How many different wavelengths are there (ignoring fine structure)?

30. (I) What are the shortest-wavelength X-rays emitted by electrons striking the face of a 33.5-kV TV picture tube? What are the longest wavelengths?

31. (I) If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tube have A = 0.030 nm. what is the voltage across the tube?

32. (I) Show that the cutoff wavelength Ao is given by 1240 nm where V is the X-ray tube voltage in volts.

33. (II) Use the result of Example 28-6 to estimate the X-ray wavelength emitted when a Co (Z = 27) atom jumps from n = 2 to n = 1.

34. (II) Estimate the wavelength for an n = 2 to n = 1 transition in iron (Z = 26).

35. (II) Use the Bohr theory to estimate the wavelength for an n = 3 to n = 1 transition in molybdenum (Z = 42). Itie measured value is 0.063 nm. Why do we not expect perfect agreement?

36. (II) A mixture of iron and an unknown material is bombarded with electrons. The wavelength of the K lines are 194 pm for iron and 229 pm for the unknown. What is the unknown material?

*37. (II) A laser used to weld detached retinas puts out 28-ms-long pulses of 640-nm light which average 0.68-W output during a pulse. How much energy can be deposited per pulse and how many photons does each pulse contain? [Hint: see Example 27-5.]

* 38. (II) A low-power laser used in a physics lab might have a power of 0.50 mW and a beam diameter of 3.0 mm. Calculate (a) the average light intensity of the laser beam, and (b) compare it to the intensity of a lightbulb producing 40-W light viewed from 2.0 m.

*39. (II) Estimate the angular spread of a laser beam due to diffraction if the beam emerges through a 3.0-mm-diameter mirror. Assume that A = 694 nm. What would be the diameter of this beam if it struck (a) a satellite 300 km above the Earth, or (b) the Moon? [Hint: see Section 25-7.]

* 40. (II) What is the wavelength of the He-Ne laser?

41. Use the uncertainty principle to estimate the position uncertainty for the electron in the ground state of the hydrogen atom. [Hint: determine the momentum using the Bohr model of Section 27-12 and assume the momentum can be anywhere between this value and zero.] How does this result compare to the Bohr radius?

42. An electron in the n = 2 state of hydrogen remains there on average about 10-8s before jumping to the n = 1 state. (a) Estimate the uncertainty in the energy of the n = 2 state. (b) What fraction of the transition energy is this? (c) What is the wavelength, and width (in nm). of this line in the spectrum of hydrogen?

43. What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell?

44. Estimate () the quantum number / for the orbital angular momentum of the Earth about the Sun. and (b) the number of possible orientations for the plane of Earth's orbit.

45. A 12-g bullet leaves a rifle at a speed of 180 m/s. (a) What is the wavelength of this bullet? (b) If the position of the bullet is known to an accuracy of 0.60 cm (radius of the barrel), what is the minimum uncertainty in its momentum?

46. Using the Bohr formula for the radius of an electron orbit, estimate the average distance from the nucleus for an electron in the innermost (n = 1) orbit of a uranium atom (Z = 92). Approximately how much energy would be required to remove this innermost electron ?

47. An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes into heat. If the specific heat of the 0.085-kg plate is 0.11 kcal/kg-C, what will be the temperature rise per minute if no cooling water is used ?

48. The ionization (binding) energy of the outermost electron in boron is 8.26 eV. (a) Use the Bohr model to estimate the effective charge Zeff, seen by this electron. (6) Estimate the average orbital radius.

49. Use the Bohr theory (especially Eq. 27-16) to show that the Moseley plot (Fig. 28-12) can be written vx -a(* - *> where Z> ~ 1, and evaluate a.

50. (a) Show that the number of different states for a given value of / is equal to 2(2/ + 1). (6) What is this number for / = 0. 1.2.3.4.5. and 6?

51. Show that the number of different electron states possible for a given value of n is In2. (See Problem 50.)

52. A beam of electrons with kinetic energy 45 keV is shot through two narrow slits in a barrier. The slits are a distance 2.0 x 10"6m apart. If a screen is placed 35.0 cm behind the barrier, calculate the spacing between the bright" fringes of the interference pattern produced on the screen.

53. The angular momentum in the hydrogen atom is given both by the Bohr model and by quantum mechanics. Compare the results for n = 2.

54. An 1100-kg car is traveling with a speed of (22 0.22) m/s. With what maximum accuracy can its position be determined?

55. An atomic spectrum contains a line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excited state that produced (his line.

56. Protons are accelerated from rest across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m away?

57. An electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

58. If the principal quantum number n were limited to the range from 1 to 6. how many elements would we find in nature?

59. If your de Broglie wavelength were 0.50 m. how fast would you be moving if your mass is 75.0 kg? Would you notice diffraction effects as you walk through a doorway? Approximately how long would it take you to walk through the doorway?

60. Suppose that the spectrum of an unknown element shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element is an ion with Z protons and one electron, determine Z and the element in question.

*61. Photons of wavelength 0.154 nm are emitted from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponds to the K(l line, what is the element?

* 62. Show that the diffractive spread of a laser beam, *s\/D as described in Section 28-11, is precisely what you might expect from the uncertainty principle, fHint: since the beams width is constrained by the dimension of the aperture D. the component of the lights momentum perpendicular to the laser axis is uncertain.]