Atoms with several electrons, potential energy

Click For Summary
SUMMARY

The discussion focuses on calculating the potential energy V(r) of an electron in an atom with atomic number Z, using the charge distribution of Z-1 electrons based on the ground state probability density of the hydrogen atom. The potential energy is defined by the equation V(r) = -ke²Z/r for electrons near the nucleus and V(r) = ke²Z/r for those farther away. The participants express confusion regarding the interpretation of charge distribution and its relation to the probability density function P(r)dr = (4/a₀³)r²e^(-2r/a₀)dr. Clarification is sought on how to apply these concepts to analyze the behavior of both internal and external electrons.

PREREQUISITES
  • Understanding of atomic structure and electron configurations
  • Familiarity with potential energy equations in electrostatics
  • Knowledge of probability density functions in quantum mechanics
  • Basic principles of the hydrogen atom and its ground state
NEXT STEPS
  • Study the derivation of potential energy equations for multi-electron atoms
  • Learn about the application of Dirac delta functions in charge distributions
  • Explore the implications of probability density functions in quantum mechanics
  • Investigate the behavior of electrons in different atomic orbitals
USEFUL FOR

Students of quantum mechanics, physicists analyzing atomic structures, and educators seeking to clarify concepts related to electron potential energy and charge distribution in multi-electron atoms.

fluidistic
Gold Member
Messages
3,932
Reaction score
283

Homework Statement


I don't really understand the problem wording. What do they ask me exactly? Here it goes:
Consider the potential energy V(r) of an electron in an atom whose atomic number is Z. Calculate the potential energy aproximating the distribution of charge of the others Z-1 electrons with a distribution given by the density of probability of the ground state of the hydrogen atom. Analize the behavior for the most internal electrons (r<< a_0) and for the most external ones (r>>a_0).

Homework Equations


V(r)=-\frac{ke^2Z}{r} or V(r)=\frac{ke^2Z}{r} if I consider only 2 electrons rather than proton vs electron.
P(r)dr=\frac{4}{a_0 ^3}r^2 e^{-2r/a_0}dr.

The Attempt at a Solution


I'm not even sure about the word distribution. I have in mind Dirac's deltas. What has it to see with P(r)dr that I gave above?
I must calculate the potential energy of the electrons that are close to the nucleous and the ones that are far from it?
 
Physics news on Phys.org
How do I do that? I know the potential of an electron in a atom, but how to use the distribution given? I'm really confused. Can someone help me?
 

Similar threads

Verify the average value of (1/r) for a 1s electron in the Hydrogen atom
  • · Replies 6 ·
Replies
6
Views
5K
Discrepancies in Electron Wavefunction Probability Calculation?
  • · Replies 7 ·
Replies
7
Views
2K
Spherically symmetric states in the hydrogen atom
  • · Replies 2 ·
Replies
2
Views
2K
Energy gaps for quasi-free electrons in a 2D lattice
  • · Replies 1 ·
Replies
1
Views
1K
Find the possible outcomes of ]##L^2## and ##L_{z}##
  • · Replies 21 ·
Replies
21
Views
2K
Approximating Probability for a Wave Function
  • · Replies 2 ·
Replies
2
Views
1K
What is the Perturbation in the Modified Coulomb Model of a Hydrogen Atom?
  • · Replies 6 ·
Replies
6
Views
4K
Calculating potential energy of hydrogen atom
  • · Replies 4 ·
Replies
4
Views
4K
Wave function in a hydrogen atom : normalization
  • · Replies 2 ·
Replies
2
Views
2K
How Does a Massive Photon Affect Hydrogen Atom Energy Levels?
  • · Replies 1 ·
Replies
1
Views
3K