Clarification of (misleading?) potential energy diagram

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SUMMARY

The discussion clarifies the potential energy diagram related to the Bohr radius (##r_{0}##) of the first electron, emphasizing that at ##r_{0}##, the potential energy is approximately ##-27 eV##. The contributor suggests that the curve depicted in the diagram represents energy (##E##) rather than potential energy (##U##), highlighting a common misconception in visual representations. They also address the pedagogical choice of depicting wavefunctions at energy levels, asserting that this practice is justified as it encapsulates all necessary information regarding energy through wavelength. The contributor confirms that their calculations align with established values, reinforcing the accuracy of their assertions.

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etotheipi
I've seen this figure kicking around, and just wanted to check that I'm not going mad. ##r_{0}## is supposed to be the Bohr radius of the first electron.

1583783363572.png

I don't think this is quite right, since at ##r_{0}## the potential energy is about ##-27eV## or something, so I think they've actually drawn the curve of ##E##. I would instead draw something like this (where T has been added for clarity):

1583783459393.png


with the original red line ##E=\frac{U}{2} = -T##. Is this a justified correction? I'm just asking because there are a lot of images on google which seem to conflate ##E## and ##U## on diagrams, and it's causing me to doubt myself a little... thank you!

Also, as a sort of follow up question, some authors when considering e.g. a particle in a box choose to draw the wavefunction at the level of the energy level. Is this a purely pedagogical choice, since evidently all of the information pertaining to the energy is already encoded in the wavelength?
 
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Thanks, that is indeed a lot better. I calculated about ##50\text{pm}## for the Bohr radius and that does indeed correspond to about ##-27\text{eV}## on that diagram.
 

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