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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
Dec
30
comment Understanding mathematically the free expansion process of an ideal gas
Thanks, I am not familiar with the Helmholtz equation but I will look into it for some extra reading, cheers.
Dec
29
accepted Understanding mathematically the free expansion process of an ideal gas
Dec
29
awarded  Supporter
Dec
29
comment Understanding mathematically the free expansion process of an ideal gas
Thank you, I'm just working through this now to make sure I understand properly.
Dec
29
revised Understanding mathematically the free expansion process of an ideal gas
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Dec
29
revised Understanding mathematically the free expansion process of an ideal gas
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Dec
29
awarded  Editor
Dec
29
revised Understanding mathematically the free expansion process of an ideal gas
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Dec
29
asked Understanding mathematically the free expansion process of an ideal gas