### Calculating the probability of finding an electron at a certain location

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**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?

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?