# Does the energy of an electron vary in the sublevels?

• B
In summary: Also, the energies will be different for different types of atoms (i.e., different chemical elements). In summary, Bohr's atom has discrete energy levels that an Electron can orbit at, with each level containing n number of sublevels. The sublevel that the Electron is in does not affect its mass. An electron in energy level l and sublevel d does not necessarily have more energy than an electron in level l sublevel s. The number of sublevels is not the relevant quantity, rather
TL;DR Summary
Does the energy of an electron have to do with the sublevel it's in?
So I read that Bohr's atom has discrete energy levels that an Electron can orbit at and that each level has n amount of sublevels (if n = 2 then there are 2 sublevels). Does the sublevel that the Electron is in have to do with it's mass? Does an electron in energy level l and sublevel d have more Energy than an electron in level l sublevel s?

Where? Please give a specific reference.

that Bohr's atom has discrete energy levels that an Electron can orbit at

Yes. (Note, though, that the Bohr atom is an outdated model that is not used in modern QM.)

and that each level has n amount of sublevels (if n = 2 then there are 2 sublevels).

I don't know what you're referring to here.

PeterDonis said:
Where? Please give a specific reference.

Quantum by Manjit Kumar
PeterDonis said:
Yes. (Note, though, that the Bohr atom is an outdated model that is not used in modern QM.)
I don't know what you're referring to here.

I read that there are energy levels n = 1, n = 2 (...) and that each energy level contained n amount of sublevels, so n = 2 is made up of two sublevels and n = 3 is made of 3 sublevels etc. Is this correct?

Quantum by Manjit Kumar

This looks like a pop science book, not a textbook, so I would not rely on it if you are actually trying to learn QM.

I read that there are energy levels n = 1, n = 2 (...)

This is correct.

each energy level contained n amount of sublevels, so n = 2 is made up of two sublevels and n = 3 is made of 3 sublevels etc

This does not look like anything I'm familiar with from QM. Does the book give any more detail about what "sublevels" are?

This does not look like anything I'm familiar with from QM. Does the book give any more detail about what "sublevels" are?

I can’t find the page in the book, but here's a chart from google. As you can see each level has n number of sublevels.

The "sublevels" described in that diagram are there, yes, although "sublevels" is not a term I've seen used to describe them. The more usual term is "orbitals". The relevant quantity is not really the number of sublevels but the number of electrons. See below.

Does the sublevel that the Electron is in have to do with it's mass?

No. All electrons have the same mass. Only a limited number of electrons can fit into each orbital, so as an atom has more and more electrons, the orbitals with lower values of ##n## fill up, and electrons have to go into orbitals with higher values of ##n##.

Does an electron in energy level l and sublevel d have more Energy than an electron in level l sublevel s?

The energy level ##n = 1## does not have any d orbitals. It only has an s orbital. You have to go to ##n = 3## before you have any d orbitals.

To a first approximation, electrons in all orbitals with the same ##n## have the same energy. However, there are a number of corrections which are different for the different types of orbitals, so if your measurements are accurate enough, you can detect the difference in energies between electrons in s, p, d, etc. orbitals in a given atom. Also, the energies will be different for different types of atoms (i.e., different chemical elements).

Quantum by Manjit Kumar
It's a good book, but it's the history of the development of QM, so you can't learn actual QM from it.

PeterDonis said:

The "sublevels" described in that diagram are there, yes, although "sublevels" is not a term I've seen used to describe them. The more usual term is "orbitals". The relevant quantity is not really the number of sublevels but the number of electrons. See below.
No. All electrons have the same mass. Only a limited number of electrons can fit into each orbital, so as an atom has more and more electrons, the orbitals with lower values of ##n## fill up, and electrons have to go into orbitals with higher values of ##n##.
The energy level ##n = 1## does not have any d orbitals. It only has an s orbital. You have to go to ##n = 3## before you have any d orbitals.

To a first approximation, electrons in all orbitals with the same ##n## have the same energy. However, there are a number of corrections which are different for the different types of orbitals, so if your measurements are accurate enough, you can detect the difference in energies between electrons in s, p, d, etc. orbitals in a given atom. Also, the energies will be different for different types of atoms (i.e., different chemical elements).
Ohh ok. Thanks for the explanation

berkeman
In the most simple non-relativistic model of the hydrogen atom each energy level ##E_n=-1 \text{Ry}/n^2## (##n \in \mathbb{N}=\{1,2,\ldots\}##) is ##2n^2##-fold degenerate (##n^2## from the possible values of ##\ell \in \{0,1,\ldots,n-1 \}## with ##2 \ell +1## values ##m \in \{-\ell,-\ell+1,\ldots,\ell \}## and another factor ##2## for two spin states ##m_s \in \{1/2,-1/2\}##).

This is what's in the table in #5. Of course, in general, the Bohr-Sommerfeld model doesn't provide a good explanation nor a good qualitative picture of the hydrogen atom (which, e.g., is in its ground state not a little flat disk but a sphere), but it can give at least an explanation for the ##n^2##-fold degeneracy (because spin wasn't known at the time they didn't know about the additional factor 2) of the non-relativistic model. Already the relativistic treatment in the Bohr-Sommerfeld model leads to a partial lift of the degeneracy, giving by some accident (I find difficult to explain though) the right fine structure even without the correct notion of spin 1/2 and the Dirac equation...

BTW: Kumar's book is popular-science book on the history of quantum mechanics, and as such not too bad, but if you want to learn quantum theory, I highly recommend not to follow the very confusing historical way, because QT is really a revolutionary step from classical physics. It's better to first learn the modern quantum theory (in the shutup-and-calculate interpretation ;-))) to build the right intuition from the very beginning. Later, it's also important to read about the history to understand, how revolutionary QT really is.

## 1. Does the energy of an electron vary in the s sublevel?

Yes, the energy of an electron can vary within the s sublevel. The s sublevel contains one orbital, and each orbital can hold a maximum of 2 electrons. The energy of an electron in the s sublevel is determined by its distance from the nucleus.

## 2. How does the energy of an electron change in the p sublevel?

The energy of an electron in the p sublevel can vary depending on its orientation in space. The p sublevel contains 3 orbitals, each with a different orientation (px, py, pz). The energy of an electron in each orbital is determined by its distance from the nucleus and its orientation.

## 3. Is the energy of an electron constant in the d sublevel?

No, the energy of an electron in the d sublevel can vary. The d sublevel contains 5 orbitals, each with a different orientation. The energy of an electron in each orbital is determined by its distance from the nucleus and its orientation.

## 4. How does the energy of an electron change in the f sublevel?

Similar to the d sublevel, the energy of an electron in the f sublevel can vary. The f sublevel contains 7 orbitals, each with a different orientation. The energy of an electron in each orbital is determined by its distance from the nucleus and its orientation.

## 5. Can an electron have the same energy in different sublevels?

No, an electron cannot have the same energy in different sublevels. The energy of an electron is determined by its distance from the nucleus and its orientation, both of which are unique for each sublevel. Therefore, an electron in one sublevel will have a different energy than an electron in another sublevel.

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