Probability/Schrodinger's equation

[NicolasM]

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 2$a_{o}\ =\ 0.5291772083(19)\ \times\ 10^{-10}α\ m$?

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

 

[Dick]

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 2$a_{o}\ =\ 0.5291772083(19)\ \times\ 10^{-10}α\ m$?

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.