bei48482_FM

Answers to Odd-Numbered Exercises 519

in this region because of its higher speed, hence has a smaller amplitude there

than near xL.

17. L^2  3 L^2  2 n^2 ^2.


18. 1 n.


19. (2L)^3 ^2


20. (nx^2 ny^2 nz^2 )(^2 ^2  2 mL^2 ); E 3 D 3 E 1 D.


21. 0.95 eV.


22. The oscillator cannot have zero energy because this would mean it is at rest in
    a definite position, whereas according to the uncertainty principle a definite po-
    sition corresponds to an infinite momentum (and hence energy) uncertainty.


23. x0 and x^2 Ekfor both states.


24. (a) 2.07 10 ^15 eV; no. (b) 1.48 1028.


25. (a) There is nothing in region II to reflect the particles, hence there is no wave
    moving to the left. (b) Hint:Make use of the boundary conditions that III
    and dIdxdIIdx at x0. (c) Transmitted current /incident currentT

(^89) , hence the transmitted current is (^89) mA0.889 mA and the reflected current
is^
1
9 mA0.111 mA.
CHAPTER 6

1. An atomic electron is free to move in three dimensions; hence, as in the case of
   a particle in a three-dimensional box, three quantum numbers are needed to de-
   scribe its motion.


2. Bohr model:Lmvr. Quantum theory: L0.


3. Only when L0, since Lzis otherwise always less than L.


4. 0, 1, 2, 3, 4.


5. 29 percent, 18 percent, 13 percent.


6. Hint:Solve dPdr0 for r.


7. 9 a 0.


8. 1.85


9. (a) 68 percent. (b) 24 percent.


10. 1.34 T.

CHAPTER 7

1. (a) 1.39 10 ^4 eV (b) 8.93 mm.


2. 54.7°; 125.3°.
   5.^42 He atoms contain even numbers of spin ^12 particles, which pair off to give zero
   or integral spins for the atoms. Such atoms do not obey the exclusion principle.
   3
   2 He atoms contain odd numbers of spin-^
   1
   2 particles and so have net spins of^

1

2    ,

(^32) , or (^52) , and they obey the exclusion principle.

7. An alkali metal atom has one electron outside closed inner shells; a halogen atom
   lacks one electron of having a closed outer shell; an inert gas atom has a closed
   outer shell.


8. 
   
   
   
   14. 
       
   
   
   
   


9. 
   
   
   
   182. 
        
   
   
   
   


10. The outermost of these electrons are, in the stated order, farther and farther from
    their respective nuclei with hence less and less tightly bound.


11. (a) 2 e, relatively easy. (b) 6 e, relatively hard.


12. C1ions have closed shells, whereas a C1 atom lacks an electron of having a
    closed shell and the relatively poorly shielded nuclear charge tends to attract an

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