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 Nov 24 awarded Notable Question Apr 27 awarded Popular Question Apr 17 awarded Curious Apr 17 revised Schwarzschild metric circular orbits and kepler's 3rd law edited title Apr 17 revised Schwarzschild metric circular orbits and kepler's 3rd law added 2 characters in body Apr 16 revised Schwarzschild metric circular orbits and kepler's 3rd law edited tags Apr 16 asked Schwarzschild metric circular orbits and kepler's 3rd law Apr 15 awarded Famous Question Feb 9 awarded Popular Question Apr 7 accepted Calculating the most probable radius for an electron of a hydrogen atom in the ground state Apr 7 comment Calculating the most probable radius for an electron of a hydrogen atom in the ground state Thanks this is what made it click for me. Apr 7 comment Calculating the most probable radius for an electron of a hydrogen atom in the ground state Ok so I understand some of what you are both saying, that the probability density * the volume enclosed by two spheres allows me to get to the answer. But it still doesn't make intuitive sense to me that the volume between two spheres (spherical shell) is used and not the volume of a sphere from the centre to some arbitrary distance r. I can remember to do this in future, but if the distribution is spherically symmetric why not use a volume element of a sphere instead of a spherical shell? Apr 7 comment Calculating the most probable radius for an electron of a hydrogen atom in the ground state Thanks but I am still confused. I have the following formula $P(r)=\int^{2\pi}_0 \int^{\pi}_0|\psi(r)|^2r^2\sin\theta\mathrm{d}\theta\mathrm{d}\varphi=|\psi(r)|^‌​2 4\pi r^2$. Which I thought to be the probability of finding the electron on a radius r and also the surface area of a sphere. Then I can proceed to find the maximum by computing $\frac{\mathrm{d}P}{\mathrm{d}r}=0$. If I accept that it is instead a volume of a spherical shell element (which I think I get now) I still do not get why a spherical shell element is used and not the volume element of a sphere itself? Apr 7 asked Calculating the most probable radius for an electron of a hydrogen atom in the ground state Apr 2 awarded Notable Question Nov 26 awarded Notable Question Sep 21 awarded Popular Question Jul 21 awarded Popular Question Dec 31 accepted Adiabatic process of an ideal gas derivation Dec 31 asked Adiabatic process of an ideal gas derivation