# Electron configuration questions

#### WMDhamnekar

Hello,
What is the meaning of highlighted statements in the attached file? I know the principal quantum number, azimuthal quantum number, magnetic quantum number, used to describe the location of electrons in an atom of any substance. I know the formula for computing amount of energy in an atom with an electron at some value n.

$E_n=\frac{Rhc}{n^2}$ where R=Rydberg constant a value of $1.097\times10^7m^{-1}$

c=speed of light 299792458 m/s.

Plank's constant
$6.63 \times 10^{-34}j*s$

Principal quantum number, no unit.

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#### studiot

Difficult to answer this since you say you know what the various quantum numbers are so presumably know that what s, p, d etc orbitals are and how they arise.

You should further distinguish between the Bohr theory and the Quantum theory.
You article does not do this but again it is hard to comment without context.

#### topsquark

Forum Staff
Hello,
What is the meaning of highlighted statements in the attached file? I know the principal quantum number, azimuthal quantum number, magnetic quantum number, used to describe the location of electrons in an atom of any substance. I know the formula for computing amount of energy in an atom with an electron at some value n.
If you are asking how to find out which shells sit at higher energies than others based on their s, p, d, etc. numbers don't worry about it. You need to use perturbation theory in QM to find those out. For all I know you might have to memorize some of it but you'll never have to actually calculate it.

-Dan

#### WMDhamnekar

Difficult to answer this since you say you know what the various quantum numbers are so presumably know that what s, p, d etc orbitals are and how they arise.

You should further distinguish between the Bohr theory and the Quantum theory.
You article does not do this but again it is hard to comment without context.
Hello,
The energy of a n=1 in a hydrogen-like electron system,is 2.17987196969e-18 J. ...(1)

When n=2, it is 5.449679924e-19J....(2)

When n=3, it is2.422079966e-19J. ... (3)

When n=4, it is 1.362419981e-19J....(4)
So suppose, an electron resides in n=1(principal quantum number), then its enery is (1). Whereas the energy of other subshell namely n=2,n=3,n=4... etc is zero. i-e $1s>2s=2p$
But article says $1s<2s=2p<3s=3p=3d<4s=4p=4d=4f<...$ which is contradictory.
But in the case of multielectron atom, author of article says correctly.

Last edited:

#### topsquark

Forum Staff
Hello,
The energy of a n=1 in a hydrogen-like electron system,is 2.17987196969e-18 J. ...(1)

When n=2, it is 5.449679924e-19J....(2)

When n=3, it is2.422079966e-19J. ... (3)

When n=4, it is 1.362419981e-19J....(4)
So suppose, an electron resides in n=1(principal quantum number), then its enery is (1). Whereas the energy of other subshell namely n=2,n=3,n=4... etc is zero. i-e $1s>2s=2p$
But article says $1s<2s=2p<3s=3p=3d<4s=4p=4d=4f<...$ which is contradictory.
But in the case of multielectron atom, author of article says correctly.
If you are dealing with a "hydrogen like" atom (an atom with just one electron) then everything works out nicely. But if there is more than one electron we have to deal with the force between any two electrons, shielding of the nuclear charge by one or more of the electrons, etc.. It becomes a real jumble of terms and you can get some fairly complex behavior. So it is quite possible that the energy contributions of a multi-electron atom will have different behaviors than in a one electron atom.

-Dan

#### studiot

Hello,
The energy of a n=1 in a hydrogen-like electron system,is 2.17987196969e-18 J. ...(1)

When n=2, it is 5.449679924e-19J....(2)

When n=3, it is2.422079966e-19J. ... (3)

When n=4, it is 1.362419981e-19J....(4)
So suppose, an electron resides in n=1(principal quantum number), then its enery is (1). Whereas the energy of other subshell namely n=2,n=3,n=4... etc is zero. i-e $1s>2s=2p$
But article says $1s<2s=2p<3s=3p=3d<4s=4p=4d=4f<...$ which is contradictory.
But in the case of multielectron atom, author of article says correctly.

Well those figures work out just fine.

The only problem is that you have missed out a negative sign from your energy equation.

The energy gets more and more negative the closer the electron approaches the nucleus.

#### WMDhamnekar

Well those figures work out just fine.

The only problem is that you have missed out a negative sign from your energy equation.

The energy gets more and more negative the closer the electron approaches the nucleus.
Hello,
So, the conclusion is what the author want to say by those highlighted statements in the attached article is unclear.

#### studiot

Hello,
So, the conclusion is what the author want to say by those highlighted statements in the attached article is unclear.
Well yes I think we already agreed that the excerpt you posted is unclear or worse since the author mixes up Bohr and Quantum theory.

But I think you are also not being clear insofar as you have not indicated whether you understood my explanation.

#### WMDhamnekar

Well yes I think we already agreed that the excerpt you posted is unclear or worse since the author mixes up Bohr and Quantum theory.

But I think you are also not being clear insofar as you have not indicated whether you understood my explanation.
Hello,
After studying the author's highlighted statements again, I think author want to say that for a hydrogen-like electron system, the energies of the subshell depends only on Principal quantum number. e.g. if electron resides in nth subshell,then its energy will be be greater than all the (n-1)th, (n-2)th....1st subshell.i-e $1s<2s=2p<3s=3p=3d<4s=4p=4d=4f...$ and so on.
In your post #2, you mentioned that i should distinguish between Bhor theory and quantum theory. But right now, i don't want to do that. Because i want to study periodic trends in periodic table,Lewis diagrams and structures, chemical reactions, stoichiometry, Acid-Base chemistry and many other topics

#### studiot

Hello,
After studying the author's highlighted statements again, I think author want to say that for a hydrogen-like electron system, the energies of the subshell depends only on Principal quantum number. e.g. if electron resides in nth subshell,then its energy will be be greater than all the (n-1)th, (n-2)th....1st subshell.i-e 1s<2s=2p<3s=3p=3d<4s=4p=4d=4f... and so on.
In your post #2, you mentioned that i should distinguish between Bhor theory and quantum theory. But right now, i don't want to do that. Because i want to study periodic trends in periodic table,Lewis diagrams and structures, chemical reactions, stoichiometry, Acid-Base chemistry and many other topics
So am I wasting my time here?

You asked a specific question and I gave you a very specific answer.

You have not referred to my answer at all.

I also addressed you second rather muddled question in which I attempted to help you because it is clear from your extract of someone else's text that they have stated incorrect material and confused you.

If you do not want to be pointed in the right direction, just say so.

For the benefit of others,
Rydberg was a spectroscopist of some note.
Planck produced the first quantisation proposal, applied to waves.
Bohr (1913) produced a different quantisation, applied to the electronic structure of the hydrogen atom, designed to fit the spectroscopic data from Rydberg.
His theory introduced circular orbits.
Bohr's proposal fit Rydberg's data rather well and was very simple, being based on classical interactions.
Nowhere in Bohr's theory is there any mention of orbitals, s, p d etc. This did not come till later.
Sommerfield modified Bohr theory to elliptic orbits and introduced relativity to the subject.
De Broglie (1917) produced the 'pilot wave theory' as the next development in quantum theory.

The results of this whole sequence of developments is now known as 'old quantum theory'

1924 saw the proposals from Schrodinger and Heisenberg which introduced orbitals (note carefully not orbits) and principal subsidiary quantum numbers.
This is known as new or modern quantum mechanics.
This was the theory that allowed quantum interpretation of chemical bonding and the periodic table.

Since you don't want to hear about all this from me I suggest the most recent presentation of all this towards the modern view (including a derivation and comparison of the equations of Bohr, Sommerfield, DeBroglie, Schrodinger and Heisenbereg) that I know of is contained in

Fundamentals of Modern Physics

By Eisberg.

This stuff tends not to be taught these days, as it is getting long in the tooth.