Calculating the probability of finding an electron at a certain location

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Paula Dowdell 1F
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Joined: Tue Nov 15, 2016 3:00 am

Calculating the probability of finding an electron at a certain location

Postby Paula Dowdell 1F » Sun Oct 29, 2017 1:23 pm

Hi! I am having some trouble understanding this concept.
In the textbook Example 2.1 shows how to calculate the probability of finding an electron, but I am still confused.

The question/answer for the problem is as shown below: Can someone walk me through this?

Q: Suppose an electron is in a 1s orbital of a hydrogen atom. What is the probability of finding the electron in a small region a distance a(sub 0) from the nucleus relative to the probability of finding it in the same small region located right at the nucleus?

A:
[probability density at r= a(sub 0)] / [probability density at r=0] = [ψ^2(asub 0)] / [ψ^2(0)]

[ψ^2(asub 0)] / [ψ^2(0)] = [(N^2) (e^(-2asub 0/asub 0))] / (N^2(0)) = e^-2 = 0.14

How did they get 0.14?

Chem_Mod
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Re: Calculating the probability of finding an electron at a certain location

Postby Chem_Mod » Sun Oct 29, 2017 3:58 pm

e-2 = 0.135 = 0.14

Note:
This is not part of the Chem 14A syllabus.
See "Outline 2: The Quantum World" on my class website for details.
Focus on the homework problems I assigned.


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