Energy and Orbit Radius for Multielectron Atoms: Lithium's N=1 Electrons

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SUMMARY

The discussion focuses on calculating the energy and orbit radius of lithium's n=1 electrons, treating one electron as a single electron in a one-electron atom with atomic number z=3. The orbit radius is determined using the formula r = [(n^2)a_0]/z, resulting in r = 1.76E-11 meters. The energy is calculated as E = -[(z^2)(13.6 eV)]/(n^2), yielding E = -112.4 eV. Additionally, the repulsive energy between the two n=1 electrons is calculated using U = k(q1*q2)/d, resulting in a repulsive energy of 41 eV, which is shared equally between the electrons.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically electron configurations.
  • Familiarity with the Bohr model of the atom and the Bohr radius (a_0).
  • Knowledge of electrostatic forces and potential energy calculations.
  • Ability to apply formulas for energy levels in hydrogen-like atoms.
NEXT STEPS
  • Study the Bohr model of multi-electron atoms and its limitations.
  • Learn about the Hartree-Fock method for electron correlation in atoms.
  • Explore the concept of electron-electron repulsion in quantum systems.
  • Investigate the use of computational chemistry tools for modeling electron interactions.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying atomic structure and quantum mechanics, as well as educators and researchers interested in electron behavior in multi-electron systems.

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Homework Statement



Treat one of lithium's n=1 electrons as a single electron in a one-electron atoms of z=3.

a) Find the energy and orbit radius.

b) The other n=1 electron, being in the same spatial state, must have the same energy and radius, but we must account for the repulsion between these electrons. Assuming they are one orbit diameter apart, what repulsive energy would they share, and if each claims half this energy, what would be the energies of these two electrons?


Homework Equations



I am stuck at part b. How should i proceed?

The Attempt at a Solution



a) r = [(n^2)a_0]/z = a_0/3 = 1.76E-11, where a_0 is the bohr radius

E = -[(z^2)(13.6eV)]/(n^2) = -(9*13.6)/2 = -112.4 eV
 
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What force is providing the repulsion?
Decide on your force, and then calculate the energy caused by this force.
Then simple to calculate the shift in enegry.
 
U = k(q1*q2)/d = 41eV where d = 2r

What if each claims half this energy?
 
Last edited:

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