Heisenberg Uncertainty Principle

[jgens]

Homework Statement

An electron is confined within a region of atomic dimensions on the order to 10^-10 m. Compute the uncertainty in its momentum.

Homework Equations

N/A

The Attempt at a Solution

I know this problem involves a simple application of Heisenberg's uncertainty principle; however, I'm having a hard time deciding what I should use as my uncertainty in the position of the particle. Could someone help me reason this out?

Thanks

 

[anathema]

for your question! It's great that you are thinking about how to apply the uncertainty principle to this problem. In order to calculate the uncertainty in momentum, we need to first determine the uncertainty in position.

In this case, the electron is confined within a region of atomic dimensions, which we can approximate to be on the order of 10^-10 m. This means that the uncertainty in position is also on the order of 10^-10 m.

Now, we can use the uncertainty principle, which states that the product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 4π. In mathematical terms, this can be expressed as ΔxΔp ≥ h/4π.

Plugging in the values, we get Δp ≥ h/(4πΔx) = (6.626 x 10^-34 J s)/[4π(10^-10 m)] = 5.27 x 10^-25 kg m/s.

Therefore, the uncertainty in momentum for the electron confined within a region of atomic dimensions is approximately 5.27 x 10^-25 kg m/s.

I hope this helps you to understand how to apply the uncertainty principle in this situation. Keep up the good work!