Where Is the Expectation Value in a 2p Orbital?

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SUMMARY

The expectation value for a 2p orbital is calculated using the formula n²a₀, where n represents the principal quantum number and a₀ is the Bohr radius. The discussion highlights that the expectation value indicates the average position of the electron within the orbital, which is typically found beneath the maximum density region of the orbital. The participant also notes that the expectation value could refer to different coordinates, suggesting a focus on for the 2p_x orbital. This understanding is crucial for accurately predicting electron locations in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with atomic orbitals and their shapes
  • Knowledge of the Bohr model and the concept of the Bohr radius (a₀)
  • Basic proficiency in mathematical expectations and probability distributions
NEXT STEPS
  • Research the mathematical derivation of expectation values in quantum mechanics
  • Study the properties and shapes of 2p orbitals in detail
  • Learn about the significance of quantum numbers in electron configuration
  • Explore the concept of probability density functions in quantum mechanics
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Students preparing for exams in quantum mechanics, educators teaching atomic structure, and researchers interested in electron behavior within atomic orbitals.

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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>
 

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