In Earnest Eutheford\'s experiment, he fired alpha particles through a piece of
ID: 977683 • Letter: I
Question
In Earnest Eutheford's experiment, he fired alpha particles through a piece of gold foil. An alpha particle consists of a cluster of two protons and two neutrons. Proton and neutrons each have a mass of about 1.67 times 10^27 kg. The alpha particles are traveling at around 5.0 times 10^4 m/s, with an uncertainty of 5%. Given this information, what would be the uncertainty in the position of the alpha particles? Would this uncertainty be significant? 5. A wavefunction has the formula Pso = Squareroot 2 sin pix. What is the probability that the particle will be found within the region bounded bu x = 0.15 and x = 0.85?Explanation / Answer
m of alpha particle = 4*1.67*10^-27 = 6.68*10^-27 Kg
delta v = 5% of 5*10^4 m/s = 2500 m/s
use Heisenberg uncertainty principle:
delta x*delta v = h/(4*pi*m)
delta x * 2500 = (6.626*10^-34)/(4*pi*6.68*10^-27)
delta x = 3.16*10^-12 m
Answer: 3.16*10^-12 m
This is very less to be significant.
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