1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem (with solution) about Heisenberg's microscope

Tags:
  1. Jun 2, 2012 #1

    s3a

    User Avatar

    1. The problem statement, all variables and given/known data
    The problem along with its solution are included as ProblemSolution.jpg.

    2. Relevant equations
    (Eq. 1) Δx ≈ λ/(sinθ)
    (Eq. 2) Δp_x ≈ 2h(v/c)(sinθ) = 2(h/λ)(sinθ)
    (Eq. 3) Δx Δp = ħ/2

    3. The attempt at a solution
    I am confused about several things. Firstly, geometrically, what is Δx and λ? I ask because I am trying to make mathematical sense of the Δx ≈ λ/(sinθ) equation rather than just memorizing it. I am not looking for any rigorous proof or anything unecessarily challenging but just an intuitive derivation.

    Secondly, why does introducing the Δp_x ≈ 2h(v/c)(sinθ) = 2(h/λ)(sinθ) equation help in answering the question; that is, how does this equation “show that if we minimize Δx by reducing λ, this will result in a loss of information about the x-component of the electron momentum?”

    Also, if the electrons and photons are in 100% horizontal (x-axis) motion, then why don't they simply slow down in the same direction or move in the opposite direction (still on the x-axis)? (The diagram implies that photons will move along the arrow-lines that point toward the lens.)

    I also don't understand (1.5.3). Is (1.5.3) supposed be something like (Eq. 3) from above?

    I would really like to understand this problem inside-out so any help in figuring this problem out will be greatly appreciated!

    If more information is needed, just ask.

    Thanks in advance!
     

    Attached Files:

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Problem (with solution) about Heisenberg's microscope
Loading...