Where does the radial probability of an electron equation come from?

[brock321]

Hey

I am looking into how the position of an electron is found. I have seen a derivation for radial wavefunction http://farside.ph.utexas.edu/teaching/qmech/lectures/node79.html but this is too complex. Ideally, I would like a very simplified version of this which leads me to understand how it is possible to know the position of electron (the probability).

For example, in kinetic theory we derive the ideal gas equation by looking at the length of a cube etc... that explanation of how we get the ideal gas equation is very intuitive - can anyone provide a simplified version of the radial distribution function Pn,l(r)=r2Rn,l(r)2
?

or - can anyone just explain what is used inorder for us to know the position of an electron? I know it comes from wavefunctions - but where does wavefunction come from?

thanks

 

[brock321]

I worked out that the radial probability of finding an electron at the bohr radius was 5 x 10$^{-17}$

Does this sound reasonable? It seems like a very small chance!