Quantum Model of an Atom with more than one electron

In summary, the conversation discussed the accuracy and limitations of a simple model for atoms with one electron, and the need for more complex methods when dealing with multi-electron atoms. The next step in accurately calculating energy levels involves considering the Coulumb potential energy between each electron and the nucleus, as well as between each pair of electrons. This can be a complex and ongoing process, and there are various methods and approaches that can be used.
  • #1
da_steve
9
0
Hi,

I just completed an assignment modelling an atom with one electron.
The model was very simple, assuming that only coulombs law applied, then solving for standing wave solutions to the Schrodinger equation to find ionization energies.

I was astounded how accurate it was. i thought it would be maybe +/- 5% but instead it was correct within 0.5% for the first 10 atoms. It gave me a bit of an ego boost which is probably why I am asking this.

I noticed that for more than one electron the model failed spectacularly. Which got me wondering what's the next step?

My guess is its the Pauli Exclusion Principle but how is it applied?
 
Physics news on Phys.org
  • #2
For multi-electron atoms you need something like the Hartree-Fock method.

The basic problem is that you have to take into account not only the Coulumb potential energy between each electron and the nucleus, but also between each pair of electrons.
 
Last edited:
  • #3
Thanks :)
That was what i was looking for
 
  • #4
The next step is messy, and I'm not sure there's an end to the number of steps as you add more and more reality. In school one of my class assignments was to calculate the ground state energy of helium as accurately as possible, and most people including me approached this by treating the (unknown) eigenfunctions as sums of hydrogenic eigenfunctions while including the potential between the electrons in schroedinger's equation. As I recall this gets you within a few percent, and if you adjust the effective Z to minimize the energy you can get an upper bound that is within a fraction of a percent.

People spend careers and write thick books on calculating energy levels in complex ions, so it's as complicated as you want it to be.
 

1. What is the Quantum Model of an Atom with more than one electron?

The Quantum Model of an Atom with more than one electron is a theoretical framework used to describe the behavior and structure of atoms with more than one electron. It is based on the principles of quantum mechanics, which states that particles such as electrons can exist in multiple energy levels and exhibit both wave-like and particle-like properties.

2. How does the Quantum Model differ from the Bohr Model?

The Bohr Model is a simplified version of the Quantum Model that only applies to atoms with one electron. The Quantum Model takes into account the interactions between multiple electrons and their energy levels, while the Bohr Model only considers the energy levels of a single electron.

3. What is the significance of electron spin in the Quantum Model?

Electron spin is an intrinsic property of electrons that is described by the Quantum Model. It refers to the angular momentum and magnetic moment of an electron, and plays a crucial role in determining the electron's energy level and behavior within an atom.

4. How does the Quantum Model explain the chemical properties of atoms with more than one electron?

The Quantum Model explains the chemical properties of atoms with more than one electron by considering the distribution of electrons in different energy levels and their interactions with each other. This can determine the reactivity and bonding behavior of atoms, as well as the shape and orientation of molecules.

5. What are the limitations of the Quantum Model of an Atom with more than one electron?

The Quantum Model, like any scientific model, has its limitations. It cannot accurately predict the exact position and behavior of electrons, but rather provides a probability distribution of where an electron is likely to be found. It also does not take into account relativistic effects, which become more significant at higher energies and speeds.

Similar threads

I Weakly interacting electrons in an atom
    • Quantum Physics
Replies
2
Views
761
I Two hydrogen atoms and Pauli's exclusion principle
    • Quantum Physics
Replies
17
Views
2K
I About the position of electrons (uncertainty)
    • Quantum Physics
Replies
6
Views
2K
B Are electrons in atoms always in eigenstates?
    • Quantum Physics
Replies
6
Views
1K
I Why is the SE better than the KG equation for a hydrogen atom?
    • Quantum Physics
Replies
18
Views
2K
I "Wave-particle duality" and double-slit experiment
    • Quantum Physics
2
Replies
36
Views
1K
I Electromagnetic radiation, photons, quantized energy levels
    • Quantum Physics
Replies
1
Views
378
I Do atoms recoil when emitting a photon?
    • Quantum Physics
2
Replies
38
Views
3K
I The electron as a smeared charge density
    • Quantum Physics
Replies
13
Views
2K
I General solution of the hydrogen atom Schrödinger equation
    • Quantum Physics
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top