Finding energy of an electron analytically

In summary, determining the energy of an electron in a given orbital in an element is a complex task that cannot be solved analytically except for hydrogen and some fake atoms. For more complex elements, numerical methods are necessary due to it being a many-body problem. There are ongoing efforts in fields such as quantum chemistry and solid-state physics to develop better and faster approximations for this task. However, it is believed that there is no simple formula for this problem due to its complexity.
  • #1
foota
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How would you find the energy of an electron in a given orbital in an element? I'm pretty sure from what I understand that you could excite the electron and measure the wavelength of light given off and find the difference, but is there some formula that at least approximates this energy?
 
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  • #2
Formally, one may solve the Schrödinger equation. For complex elements (i.e. elements that have more than one electron present) numerical methods become necessary.
 
  • #3
It can't be done analytically for anything other than hydrogen. (And some fake atoms like 'harmonium') There are approximations for helium that can be hand-calculated, but even those are either inaccurate or tedious.

There are several whole fields of science (e.g. quantum chemistry, solid-state physics) largely devoted to finding better and faster approximations of this. So obviously: no simple "formula" is known. It's a many-body problem, so there are some mathematical reasons to believe no such simple formula exists, either. (among other things, it'd likely prove P = NP) But people are developing new methods of calculating and approximating the solutions every day, as well as applying the existing methods to learning new stuff.
 

1. What is the equation for finding the energy of an electron analytically?

The energy of an electron can be found analytically using the equation: E = -13.6/(n^2), where n is the principle quantum number.

2. How does the principle quantum number affect the energy of an electron?

The principle quantum number, n, determines the energy level of an electron. As n increases, the energy level of the electron also increases.

3. Can the energy of an electron be negative?

Yes, the energy of an electron can be negative. This indicates that the electron is in a bound state, meaning it is still attached to the nucleus of an atom.

4. How does the energy of an electron change when it moves to a higher energy level?

When an electron moves to a higher energy level, it gains energy. This can be seen in the increase in the principle quantum number, n, in the equation E = -13.6/(n^2).

5. Is the energy of an electron constant?

No, the energy of an electron is not constant. It can change based on factors such as its energy level, interactions with other particles, and its position in an electric field.

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