Uncertainty in speed


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Chem_Mod
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Uncertainty in speed

Postby Chem_Mod » Wed Apr 24, 2013 9:27 pm

The hydrogen atom has a radius of approximately 0.05 nm. Assume that we know the position of an electron to an accuracy of 1 % of the hydrogen radius, calculate the uncertainty in the speed of the electron using the Heisenberg uncertainty principle

Chem_Mod
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Re: Uncertainty in speed

Postby Chem_Mod » Wed Apr 24, 2013 9:27 pm

1% of 0.05 nm is simply: 0.01*0.05nm = 5e-4nm.

Griffin Schneider 1I
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Re: Uncertainty in speed

Postby Griffin Schneider 1I » Sun Oct 19, 2014 4:27 pm

Why is the uncertainty of the position 1% of the radius when solving? Shouldn't it be 1% of the diameter? In the worked example in the course reader, the problem states that the electron is confined to its atomic diameter, why is it different for this question?

Chem_Mod
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Re: Uncertainty in speed

Postby Chem_Mod » Mon Oct 20, 2014 9:49 am

If you notice the question states that the uncertainty in the radius is 1% -- that is the uncertainty they give you. To answer your question why is it different. Well, all questions wont be the same. We want to make sure you understand why you are plugging in the values, not just that you can plug in values... So this is a good question in that sense because it has you questioning your understanding! This is how you learn.

an example:

I know that the uncertainty in position of an object confined to 1 meter is 1%... ie the uncertainty is .01 meters, but I could have said that the uncertainty is 1% (object confined to 1/2 meter) in this case the absolute uncertainty is lower (ie. .005m) but as a fraction it is the same.

DavidEcheverri3J
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Re: Uncertainty in speed

Postby DavidEcheverri3J » Wed Oct 24, 2018 9:18 pm

Why is it asking for speed? What does speed have to do with uncertainty of position?

Asia Yamada 2C
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Re: Uncertainty in speed

Postby Asia Yamada 2C » Tue Oct 27, 2020 3:08 pm

Velocity is related to momentum because the product of velocity and mass is equal to momentum. Therefore, uncertainty in velocity is related to uncertainty in position through Heisenberg’s Indeterminacy Equation which is Δx • Δp ≥ h/4pi or Δx • Δv• m ≥ h/4pi


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