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!

Finding the probability of 1s electron within a cubical volume

  1. Nov 8, 2017 #1
    1. The problem statement, all variables and given/known data
    How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus.
    2. Relevant equations
    The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression
    $$\int_{0}^{a}\int_{0}^{\pi}\int_{0}^{2\pi}|\psi(r,,\theta,\phi)|^2r^2 dr \sin(\theta) d\theta d\phi$$
    but how to find probability within a cubic region?

    3. The attempt at a solution
    I thought I could transform ${(r,\theta,\phi)}$ into (x,y,z) coordinates and integrate the above integral within proper limits, but the integral will become messy! and also I don't know whether it is the proper way of doing this problem, all I am asking is give me a hint how to do this problem?
     
  2. jcsd
  3. Nov 9, 2017 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You could approximate it by choosing a sphere of the same volume.
     
  4. Nov 9, 2017 #3

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Considering the size of the cube, will the value of the wavefunction be approximately constant throughout the cube?
     
  5. Nov 10, 2017 #4
    Yes the value of wavefunction will be approximately constant throughout the cube.
     
  6. Nov 10, 2017 #5
    so it is enough to find the probability density at 50pm times the volume of cube right?
     
  7. Nov 10, 2017 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the probability of 1s electron within a cubical volume
Loading...