The-Mexican™
California, United States
 
 
The Probability of finding the electron in the region of space described by the folowing wavefunction:

Ψ = (r-2)/(a0)* e^( -r/ 2a0 ) Note: a0 is a constant @ 52.9 pico meters.

N^2 ∫ r*Ψ^2 dΓ

where d Γ = r*dr*SinθdθdΦ

Integrating from the nucleus to infinity we expect the probability to be 1, thus.

N^2 ∫ r*Ψ^2 dΓ = 1 (from 0 to infinity)

The normalization constant n is determined to be:

N = 0.00015108582968844148

Thus integrating in the region of 200 to 400 pm.

N^2 ∫ r*Ψ^2 dΓ = 0.5462834607306051

54.6% chance of finding the electron in the region of 200pm to 400pm from the nucleus.

Note that these results are based on the probability of finding "an electron," at this point I assume you know what element I am talking about...
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