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Uncertainty

QUESTION: The speed of bullet with a mass = 0.050 kg and speed = 420 m/s. Uncertainty = 0.010%.. What is the minimum uncertainty in the bullet's position if is measured at the same time as the speed is measured?
Choices to pick from:
(a) 2.5 x 10-31 m
(b) 5.0 x 10-32 m
(c) 7.5 x 10-33 m
(d) 2.5 x 10-34 m
(e) 6.0 x 10-36 m

Answer

The uncertainty in momentum is 0.01% of 0.05x420 = 21x0.01/100 = 0.0021

The uncertainty in position = Planck's constant/[2p x Uncertainty in momentum]
= 6.63x10-34/[6.28 x0.0021] = 5.02x1032 m

The answer is (b).
 
 
 
© Keith Gibbs 2011