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

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In summary, to find the energy and orbit radius of a lithium atom's n=1 electron, we use the equations r = [(n^2)a_0]/z and E = -[(z^2)(13.6eV)]/(n^2), where a_0 is the Bohr radius and z=3 for lithium. When considering the repulsion between two n=1 electrons in the same spatial state, we can calculate the repulsive energy using U = k(q1*q2)/d, where d is the distance between the two electrons. If each electron claims half of this energy, the resulting energy for each electron would be 41eV. To proceed with solving this problem, one must decide on
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aznkid310
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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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  • #2
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.
 
  • #3
U = k(q1*q2)/d = 41eV where d = 2r

What if each claims half this energy?
 
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FAQ: Energy and Orbit Radius for Multielectron Atoms: Lithium's N=1 Electrons

How do multielectron atoms differ from single electron atoms?

Multielectron atoms have more than one electron in their outer shells, while single electron atoms only have one. This means that multielectron atoms have more complex electronic configurations and interactions between electrons, resulting in different properties and behaviors.

How does the number of electrons affect the energy levels in a multielectron atom?

The number of electrons in a multielectron atom determines the number of energy levels and sublevels available. The energy levels can be thought of as "shells" while the sublevels are "orbitals" within each shell. As the number of electrons increases, the energy levels become more closely spaced and the sublevels become more complex.

What is the significance of the Aufbau principle in multielectron atoms?

The Aufbau principle states that electrons will occupy the lowest available energy level first before moving to higher levels. In multielectron atoms, this principle helps to predict the electronic configuration and stability of the atom. It also explains why some elements have unique properties due to their electronic configurations.

How do multielectron atoms exhibit quantum mechanical behavior?

Like all atoms, multielectron atoms exhibit quantum mechanical behavior, meaning that the behavior and properties of electrons cannot be precisely determined and can only be described by probabilities. This is due to the wave-like nature of electrons and the uncertainty principle in quantum mechanics.

What are some applications of studying multielectron atoms?

The study of multielectron atoms has many practical applications, such as in the development of new materials, understanding chemical reactions, and designing electronic devices. It also helps to explain the behavior of complex molecules and can aid in the development of new technologies, such as quantum computing.

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