Given an electron with mass 9.1×10−31kg is moving along x-axis with velocity 106ms−1 and passes through a screen with slit Δy=10−9. Is it possible to find the uncertainty of angle between the final vector and the x-axis?
My attempt:
- Finding the uncertainty of momentum Δp by using the Heisenberg's uncertainty principle.
- Solving the uncertainty of angle with the momentum along x-direction px, by using tan(Δθ)=Δpypx
I doubt step(2) because we are looking for uncertainty but not the angle itself. I have no idea about the uncertainty.
Answer
I think you are missing something.
According to Heisenberg's uncertainty principle,
ΔyΔpy∼ℏ
If Δvy is the uncertainty in velocity along the y- direction, then
mΔyΔvy∼ℏmΔyvxΔθ∼ℏΔθ∼ℏmvxΔy
where we have taken Δθ be the uncertainty in the angle between the x- and y- component of velocities.
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