bei48482_FM

Answers to Odd-Numbered Exercises 517

electron’s final kinetic energy is p^2 c^2 m^2 c^4 mc^2 pc, so the process can-

not occur while conserving both momentum and energy.

21. 2.4 1018 Hz; x-rays.


22. 2.9°.


23. 5.0 1018 Hz.


24. C5.8 10 ^8 nm0.1 nm.


25. 1.5 pm.


26. 2.4 1019 Hz.


27. 64°.


28. 335 keV.


29. 0.821 pm.


30. (b) 2.3.


31. 8.9 mm.


32. 11 cm.


33. 0.015 mm.


34. 1.06 pm.


35. (a) 1.9 10 ^3 eV. (b) 1.8 10 ^25 eV. (c) 3.5 1018 Hz; 7.6 kHz.


36. (a) e 2 GMR.(b) R 2 GMc^2.

CHAPTER 3

1. The momenta are the same; the particle’s total energy exceeds the photon energy;
   the particle’s kinetic energy is less than the photon energy.


2. 3.3 10 ^29 m.


3. 4.8 percent too high.


4. 0.0103 eV; a relativistic calculation is not needed.


5. 5.0 V.


6. The electron has the longer wavelength. Both particles have the same phase and
   group velocities.


7. p2.


8. 1.16c; 0.863c.


9. (b) p1.00085c; g0.99915c.


10. Increasing the electron energy increases the electron momentum and so decreases
    the de Broglie wavelength, which in turn reduces the scattering angle .


11. (a) 4.36 106 m/s outside; 5.30 106 m/s inside. (b) 0.167 nm outside;
    0.137 nm inside.


12. 2.05n^2 MeV; 2.05 MeV.


13. 45.3 fm.


14. Each atom in a solid is limited to a certain definite region of space—otherwise
    the assembly of atoms would not be a solid. The uncertainty in position of
    each atom is therefore finite, and its momentum and hence energy cannot be
    zero. The position of an ideal-gas molecule is not restricted, so the uncertainty
    in its position is effectively infinite and its momentum and hence energy can
    be zero.


15. 3.1 percent.


16. 1.44 10 ^13 m.


17. (a) 24 m; 752 waves. (b) 12.5 MHz.

CHAPTER 4

1. Most of an atom consists of empty space.


2. 1.14 10 ^13 m.

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