Peoples Physics Book Version-2

http://www.ck12.org Chapter 27. Quantum Mechanics Version 2

21. The momentum of an electron is measured to an accuracy of± 5. 1 × 10 −^24 kg·m/s. What is the corresponding
    uncertainty in the position of the same electron at the same moment? Express your answer in Angstroms
    (1= 10 −^10 m, about the size of a typical atom).


22. Thor, a baseball player, passes on a pitch clocked at a speed of 45±2 m/s. The umpire calls a strike, but Thor
    claims that the uncertainty in the position of the baseball was so high that Heisenberg’s uncertainty principle
    dictates the ballcouldhave been out of the strike zone. What is the uncertainty in position for this baseball?
    A typical baseball has a mass of 0.15 kg. Should the umpire rethink his decision?


23. Consider a box of empty space (vacuum) that contains nothing, and has total energy E=0. Suddenly, in
    seeming violation of the law of conservation of energy, an electron and a positron (the anti-particle of the
    electron) burst into existence. Both the electron and positron have the same mass, 9. 11 × 10 −^31 kg.
    a. Use Einstein’s formula(E=mc^2 )to determine how much energy must be used to create these two
    particles out ofnothing.
    b. You don’t get to violate the law of conservation of energy forever – you can only do so as long as the
    violation is “hidden” within the HUP. Use the HUP to calculate how long (in seconds) the two particles
    can exist before they wink out of existence.
    c. Now let’s assume they are both traveling at a speed of 0.1 c. (Do a non-relativistic calculation.) How far
    can they travel in that time? How does this distance compare to the size of an atom?
    d. What if, instead of an electron and a positron pair, you got a proton/anti-proton pair? The mass of a
    proton is about 2000×higher than the mass of an electron. Will your proton/anti-proton pair last a
    longerorshorteramount of time than the electron/positron pair? Why?

Answers to Selected Problems

1. 
   
   
   
   1. 
      
      
      
      6. 752 × 10 −^26 J, 2. 253 × 10 −^34 kgm/s
      
      
      
      
   
   
   2. 
      
      
      
      5. 96 × 10 −^20 J, 1. 99 × 10 −^28 kgm/s
      
      
      
      
   
   
   3. 
      
      
      
      4. 90 × 10 −^28 J, 1. 63 × 10 −^36 kgm/s
      
      
      
      
   
   
   4. 1.94 eV, 1. 04 × 10 −^27 kgm/s
   
   
   5. 12.7 eV, 6. 76 × 10 −^27 kgm/s
   
   
   6. 5.00 eV, 2. 67 × 10 −^21 kgm/s
   
   
   
   

1..0827 nm

2. 
   
   
   
   4. 59 × 10 −^4 nm
   
   
   
   


3. 730 nm


4. 
   
   
   
   1. 03 × 10 −^20 m
   
   
   
   


5. 36 nm


6. no


7. 380 nm,73 nm,74 nm,36 nm,92 nm,39 nm
   3..80 V


8. 480 nm
   1..124 nm
   2..00120 nm


9. 24,600 m/s


10. 
    
    
    
    1. 84 × 108 m/s
       1..491 m/s
    
    
    
    


11. 
    
    
    
    3. 14107 J
    
    
    
    


12. 64 Mw