Quantum Numbers & Electron Energy

In summary, according to Dirac's theory, the "l" quantum number (angular momentum) affects the energy of the electron within the atom. Additionally, changing "l" also changes the energy of the electron's subshells.
  • #1
SeReNiTy
170
0
Hi i was wondering what quantum numbers can change the energy of a electron within a atom. I thought it would be n and l since its the energy and sub energy numbers, but i was wrong. Can someone explain it in some more deatail please?
 
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  • #2
For the simplest of them all,the H atom,without taking into account hyperfine structure Hamiltonian and the Lamb shift due to the interaction to virtual photons,it's EITHER "n" (Schrödinger's theory) or "n" and "j" (the latter is the sum between "l" and "s") in Dirac's relativistic theory.

The best analysis of the H & He atoms is found in [1],while in the general case,a good approach on atomic physics is found in [2].

I don't know what u mean by "sub energy numbers.

For a multielectronic atom,the problem of computing total angular momentum operator is not that simple.Read more in [3]

Daniel.

-----------------------------------------------------------------------
[1]Bethe & Salpeter:"Quantum Mechanics of One and Two Electron Atoms"
[2]R.E.Moss:"Advanced Molecular Quantum Mechanics".
[3]Bransden & Joachain:"Atom's and Molecule's Physics".
 
  • #3
I think that is way above my level now, I'm only first year university dexter! :biggrin:

Now my question was changing which of the quantum numbers will change the energy of the electron in the atom. I know that if you change the "n" number obviously the energy of the electron will change cause it has either been promoted or demoted to a higher/lower energy level but i was thinking if you change "l" the angular momentum number you should also change the energy of the electron as s,p,d,f subshells also have different energy levels as I'm led to believe! :confused:
 
  • #4
Yes,i said that in the formula of energy levels (in Dirac's theory) "l" is included indirectly by means of "j"...So varying "l" means varying "j" and therefore changing the energy level.

Daniel.
 
  • #5
dextercioby said:
Yes,i said that in the formula of energy levels (in Dirac's theory) "l" is included indirectly by means of "j"...So varying "l" means varying "j" and therefore changing the energy level.

Daniel.

So in other words your saying sticking purely to shrodingers theory only "n" changes the energy of the electron?
 
  • #6
That's right.

Daniel.

P.S.No spin involved in SE,nor relativistic effects...
 
  • #7
dextercioby said:
That's right.

Daniel.

P.S.No spin involved in SE,nor relativistic effects...

Thanks dexter, this forum is always a great resource! :smile:
 

1. What are quantum numbers and how do they relate to electron energy levels?

Quantum numbers are a set of numerical values that describe the energy, location, and spin of an electron in an atom. They are used to predict and understand the behavior of electrons in an atom, particularly in relation to their energy levels. Each electron in an atom has a unique set of quantum numbers that determine its specific energy level.

2. What are the four quantum numbers and what do they represent?

The four quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms). The principal quantum number represents the energy level of the electron, the angular momentum quantum number represents the shape of the electron's orbital, the magnetic quantum number represents the orientation of the electron's orbital, and the spin quantum number represents the spin of the electron.

3. How are quantum numbers determined for an electron?

The principal quantum number (n) is determined by the energy level of the electron, which is based on the element's atomic number. The angular momentum quantum number (l) is determined by the shape of the electron's orbital, which can be found using the azimuthal quantum number. The magnetic quantum number (ml) is determined by the orientation of the electron's orbital, which can be determined using the magnetic quantum number. The spin quantum number (ms) is determined by the spin of the electron, which can be either +1/2 or -1/2.

4. How do quantum numbers affect an electron's energy level?

The principal quantum number (n) determines the energy level of an electron, with higher values of n representing higher energy levels. The angular momentum quantum number (l) affects the energy level by determining the shape of the electron's orbital, with different shapes having different energies. The magnetic quantum number (ml) affects the energy level by determining the orientation of the electron's orbital, with different orientations having different energies. The spin quantum number (ms) does not directly affect the energy level, but it does determine the spin of the electron, which can affect its energy in certain situations.

5. How do quantum numbers and electron energy levels relate to the periodic table?

The periodic table is organized based on the electron configurations of elements, which are determined by the quantum numbers and energy levels of their electrons. Elements in the same group have similar electron configurations, meaning they have the same number of electrons in their outermost energy level. The quantum numbers of these outermost electrons determine the chemical properties of the element, which is why elements in the same group have similar chemical properties. Additionally, the periodic table can also be used to predict the energy levels of electrons in different elements based on their atomic numbers and position on the table.

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