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

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SUMMARY

The radial probability of finding an electron is derived from the radial wavefunction, specifically represented by the equation Pn,l(r) = r²Rn,l(r)². This equation quantifies the likelihood of locating an electron at a certain radius from the nucleus. The discussion highlights the complexity of deriving this function and seeks a simplified explanation, emphasizing the need for intuitive understanding similar to that of the ideal gas equation. The calculated probability at the Bohr radius is noted as 5 x 10-17, which is acknowledged as a very small chance.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wavefunctions
  • Familiarity with radial distribution functions
  • Basic knowledge of the Bohr model of the atom
NEXT STEPS
  • Study the derivation of the radial wavefunction in quantum mechanics
  • Explore the concept of probability density in quantum systems
  • Learn about the implications of the Bohr model on electron positioning
  • Investigate the relationship between wavefunctions and observable properties in quantum mechanics
USEFUL FOR

Students of quantum mechanics, physicists, and educators looking to simplify complex concepts related to electron positioning and wavefunctions.

brock321
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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
 
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I worked out that the radial probability of finding an electron at the bohr radius was 5 x 10[itex]^{-17}[/itex]

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

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