Heisenberg Post-Module #18 [ENDORSED]

[Michelle Dong 1F]

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.
Comment on your value obtained.

Would you have to multiply the diameter (1*10^-12 m) by 1% in order to find delta x? I tried doing that and it didn't give me the correct answer.

[Eli Aminpour 2K]

Normally, the problem will give you an atomic radius and you have to multiply by two to get the diameter (which becomes the uncertainty in position). But, this problem directly tells you that the uncertainty is just 1 % the radius, so there is no need to multiply by two and use the diameter. Try multiplying the given radius by 1% and plugging that into Heisenberg's equation and you should get the right answer.

[Justin Bui 2L]

I agree, knowing the radius to an accuracy of 1% means that the uncertainty in position is a hundredth of what the radius is, which is multiplying the radius by 0.01 or dividing by 100. Then, you can use that as delta x in the heisenberg equation and finish