Deriving ground state electron energy using Boundary Value

In summary, the conversation is about using the Radial Equation to solve for ##E_1## in Schrodinger's Equation. The last problem involves arbitrary constants ##n##, ##l##, and ##m##, with constraints on ##l## in the ground state of ##n=0##. The speaker also apologizes for the poor image quality of the problem.
  • #1
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Homework Statement
Derive the ground state electron energy ##E_1## based on the boundary condition of R(r) -> 0, r -> ∞ and write down the corresponding energy function, Psi. (5 points)
Relevant Equations
Schrodinger's Equation (below)
ss01.png

This is the equation given.
I attempted to use Radial Equation, obtained from separating variables, to solve for ##E_1##.
IMAG1361_2.jpg

IMAG1363_2.jpg
 

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  • #2
currently said:
Here's the problem. the equation was stated in class to be Schrodinger's Equation.
Last problem should say: n, l, and m are arbitrary constants.

View attachment 255295

We are now in part (d) of your exercise. I can hardly read, let alone quote from your jpg.
What constraints are there on ##l##, and what does that mean when in the ground state ##n=0## ?
 
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  • #3
BvU said:
What constraints are there on ##l##, and what does that mean when in the ground state ##n=0## ?
Okay, will keep in mind. Thanks!

BvU said:
We are now in part (d) of your exercise. I can hardly read, let alone quote from your jpg.
I'm slightly touched you remember which problem this is.. and I apologize for the terrible image quality! I'll be more quotable next post.
 
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Related to Deriving ground state electron energy using Boundary Value

1. What is the concept of "ground state" in electron energy?

The ground state is the lowest energy level of an electron in an atom. It is the most stable state and the one in which the electron is most likely to be found.

2. How is the ground state electron energy derived using Boundary Value?

The Boundary Value method is a mathematical technique used to solve for the energy levels of electrons in an atom. It involves setting up boundary conditions at the edges of the atom and solving a differential equation to determine the allowed energy levels.

3. What are the factors that affect the ground state electron energy?

The ground state electron energy is affected by the nuclear charge of the atom, the number of electrons in the atom's outermost energy level, and the distance of the electron from the nucleus.

4. Can the ground state electron energy be experimentally measured?

Yes, the ground state electron energy can be experimentally measured using techniques such as spectroscopy, which involves studying the wavelengths of light emitted or absorbed by the atom.

5. How does the ground state electron energy relate to an atom's chemical properties?

The ground state electron energy determines an atom's chemical properties by influencing the atom's reactivity and ability to form chemical bonds with other atoms. Atoms with lower ground state energies are more likely to participate in chemical reactions.

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