Exam 1 Answer for Question 4

Exam 1 Answer for Question 4 - 4 Consider a quantum...

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4. Consider a quantum mechanical world in which an archer is shooting arrows at cans lined up on a fence. A total of 11 cans are lined up on a horizontal beam, with the neighboring cans touching each other. Each can has a width of 1Å, a mass of 20 ng, and an uncertainty in the horizontal velocity of ± 0.105 Å/s. Each arrow has a width of 0.1Å, a mass of 0.2 ng, and an uncertainty in the horizontal velocity of ± 0.0105 Å/s. Each question is worth 5 points. a. Calculate the uncertainty of the horizontal position of each can. ! x = ! 2 m ! v = 1.05 " 10 # 34 Js 2 (2.0 " 10 # 11 kg) " (1.05 " 10 # 11 m / s ) = 2.5 " 10 # 13 m = 0.0025 Å b. Calculate the uncertainty of the horizontal position of each arrow
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Unformatted text preview: ! x = ! 2 m ! v = 1.05 " 10 # 34 Js 2 (2.0 " 10-13 kg) " (1.05 " 10 # 12 m / s ) = 2.5 " 10 # 10 m = 2.5 Å c. Assuming that the arrow is shot at the middle of the central can, calculate the probability that the can that the arrow hits, will be the central can. The uncertainty in the position of the cans is small and not important but the uncertainty in the position of the arrow is large at 5Å. Since any can within 2.5Å of the center can be hit, the 2 cans on either side of the central can may be hit, making the probability only 1 out of 5....
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  • Spring '14
  • Mass, horizontal velocity

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