Probability/Schrodinger's equation

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SUMMARY

The discussion centers on calculating the probability of finding an electron within a sphere of radius 2ao for a hydrogen atom in its ground state. The proposed formula, 0∫2α 4πr3ψ2dr/3 x100%, is incorrect due to dimensional inconsistencies. The correct approach involves using the three-dimensional integral of |ψ|2, emphasizing the need for a proper differential factor in the calculation.

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We have a hydrogen atom in its ground state. What is the probability of an electron being found within a sphere (with nucleus being the origin) of a radius of 2a_{o}\ =\ 0.5291772083(19)\ \times\ 10^{-10}α\ m?

Would 0∫2α 4πr3ψ2dr/3 x100% be correct?
 
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NicolasM said:
We have a hydrogen atom in its ground state. What is the probability of an electron being found within a sphere (with nucleus being the origin) of a radius of 2a_{o}\ =\ 0.5291772083(19)\ \times\ 10^{-10}α\ m?

Would 0∫2α 4πr3ψ2dr/3 x100% be correct?

No, it wouldn't even have correct dimensions. Why do you think that's right? Work it out from the three dimensional integral of |ψ|^2. Your differential factor is wrong.
 
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