## Pre Assessment Questions

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Kelsey Jug 1J
Posts: 38
Joined: Wed Sep 21, 2016 2:59 pm

### Pre Assessment Questions

Pre assessment question from the Heisenberg Uncertainty module:

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.

Because (delta p) = (m) x (delta v) and (delta p) x (delta x) = h / 4pi would we set up the equation as:

(9.10938 x 10^-31 kg ) x (delta v) x (0.1 nm) x (0.01) = h / 4pi and solve for (delta v) from there, or do we have to apply the 1% somewhere else?

The options are:
A. Delta v <= 104m/s , Delta v is low
B. Delta v >= 104m/s , Delta v is high
C. Delta v <= 108m/s , Delta v is low
D. Delta v >= 108m/s , Delta v is high
E. None of the above

and I keep getting "none of the above" with the method I'm using. Can anyone confirm or correct?

Alex Dib 4H
Posts: 34
Joined: Wed Sep 21, 2016 2:57 pm

### Re: Pre Assessment Questions

I'm also getting "none of the above" for this one and have been second guessing myself about it for a while too, lol. But instead of .1 nm x .01, I did .05 nm x .01 because they are saying 1% of the radius (I think we always double it when uncertainty is given in +/-. Here they are giving us a direct distance). Still not getting any of these options tho.

Thinking about this problem logically tho, since we know that electron lies in a location extremely small (5 x 10^-13 m... or if we're using .1 nm, it would be 1 x 10^-12), it wouldn't make sense for the uncertainty in velocity to be as small as 108 m/s, when electrons are traveling closer to the speed of light. I am getting an uncertainty in velocity of 1 x 10^8 m/s.

I think since we are almost certain where to find the electron, we are very uncertain about its velocity.

Please someone correct me if I'm wrong!

Chem_Mod
Posts: 18011
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 418 times

### Re: Pre Assessment Questions

Alex gave a good thought process of the uncertainty of velocity when the uncertainty of the position of the electron is small (or fairly certain where it is). Another approach would be to back calculate from the answer to find uncertainty of position. And from this, try to convince yourself with the answer.