Neurtal hydrogen atom net electric charge and electric field at Bohr radius.

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SUMMARY

The discussion centers on the misunderstanding of the net electric charge and electric field of a neutral hydrogen atom at the Bohr radius (a0). The participant questions why the total charge, represented as -e, does not equal the integral of charge density (ρ) over the volume from 0 to a0. The confusion arises from the interpretation of the Bohr radius as the boundary of the electron cloud, which is not explicitly defined in the problem. The participant concludes that the charge density must be evaluated correctly within the context of the atom's structure.

PREREQUISITES
  • Understanding of quantum mechanics, specifically the Bohr model of the hydrogen atom.
  • Familiarity with electric charge concepts and charge density (ρ).
  • Basic calculus knowledge for evaluating integrals.
  • Knowledge of atomic structure and electron cloud representation.
NEXT STEPS
  • Review the Bohr model of the hydrogen atom and its implications on electron distribution.
  • Study charge density calculations in spherical coordinates.
  • Learn about the concept of electric fields generated by point charges and distributions.
  • Examine the relationship between charge density and total charge in quantum systems.
USEFUL FOR

Students preparing for exams in quantum mechanics, physics educators, and anyone interested in the fundamental concepts of atomic structure and electric fields.

dolerka
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I am studying for my exam and I have run into this problem. The problem is given here [PLAIN]http://faculty.mint.ua.edu/~...-7_atoms_12Mar10/HW6-7_atoms_12Mar10_SOLN.pdf,[/PLAIN] it is #9.

I don't understand why -e ≠ ∫ρdV from 0 to the bohr radius, a0. If all of the charge is contained within that volume.
I may not be understanding where exactly the Bohr radius is being measured to. I am thinking the a0 is the radius of the electron cloud. So the electron cloud would be a sphere with radius a0 with a charge of -e.
 
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