Where Is the Expectation Value in a 2p Orbital?

Radfire
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Homework Statement


Where would the expectation value on a 2p orbital lie? and where would you likely find the electron relative to the maximum?


Homework Equations



found on a forum that the expectation value is n^2 a_0 but id like a more reliable source

The Attempt at a Solution



have an exam in morning and its just something which would be nice to know before i walk out the door.

using the formula gives an idea but I am not sure if that's even a proper formula. if i was to guess id say under the maximum of the "fat" part of the orbital since its an average value. and for the second part I am guessing that to would be where the orbital is thickest, even though i know an orbital is an area of probability so technically it could be everywhere at once in the orbital.
 
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Expectation value of what — r, x, y, z?
 
question doesn't say, id guessing it means the average position of an electron so maybe take 2p_x and find <x>
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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