# Conflict Between Infinite energy levels and Valence Shells

## Homework Statement

I'm having trouble understanding the existence of valence shells.

I understood that valence shell is the last energy level for the electrons to populate around an atom.

But, according to Bohr model , an atom can have infinite energy levels , so I don't understand:

How can an atom have a level , called ' valence shell ' ( which represents the last energy level for the electrons to populate an atom ) if the atom itself can have infinite energy levels ( at-least theoretically )?

## The Attempt at a Solution

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BvU
Homework Helper
2019 Award

Here at PF it's "encouraged" that folks orient themselves and ask for help when they encounter trouble.

But I'll give you a few hints/questions:
last energy level for the electrons to populate around an atom
In what order are these levels populated ?
When can the 'population process' stop ?

Borek
Mentor
according to Bohr model , an atom can have infinite energy levels
Infinite NUMBER of energy levels, not infinite energy levels.

Here at PF it's "encouraged" that folks orient themselves and ask for help when they encounter trouble.

But I'll give you a few hints/questions:
In what order are these levels populated ?
When can the 'population process' stop ?
I don't know, i'm learning chemistry for the first time that is why i'm asking.

Infinite NUMBER of energy levels, not infinite energy levels.
The bohr energy is quantified, as long as I can remmember then there was no limit which quantified energy level you can get to if you put enough energy to the system, so what I said is fine.

TeethWhitener
Gold Member
How can an atom have a level , called ' valence shell ' ( which represents the last energy level for the electrons to populate an atom ) if the atom itself can have infinite energy levels ( at-least theoretically )?
An atom might have an infinite number of energy levels, but it doesn’t have an infinite number of electrons. In the lowest energy state, the finite number of electrons will fill the lowest energy levels. This is called the aufbau principle:
https://en.m.wikipedia.org/wiki/Aufbau_principle
So why don’t all the electrons just go into the lowest energy level and be done with it? Because electrons can’t all go into the lowest energy level. It’s a phenomenon known as Pauli’s exclusion principle:
https://en.m.wikipedia.org/wiki/Pauli_exclusion_principle
Electrons are fermions, and therefore only one electron is allowed to occupy a distinct quantum state. Based on these principles (and a few others relating to angular momentum), one can see that if an atom has 15 electrons, they will tend to occupy the 15 lowest energy orbital states. The valence orbitals are simply the highest of these low energy states that are occupied by electrons. The electrons occupying these valence orbitals are important because they are the ones that contribute most heavily to chemical bonding.

CGandC
BvU
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2019 Award
I don't think this last answer is effective for someone who just sees the Bohr model for the first time ...

GC&C, have you seen the formula for the energies in the Bohr model ?

(formula picture: wikipedia | Bohr model | derivation )

The energies are negative (bound states -- zero or positive energy would mean a free electron, not in orbit) and there are an infinite number of them, but the energy is never infinite.

The Bohr model is restricted to looking at a single electron 'seeing' a positive charge at the origin. Meaning it applies reasonably well to an outer electron of an atom : an electron in the valence shell.

An atom might have an infinite number of energy levels, but it doesn’t have an infinite number of electrons. In the lowest energy state, the finite number of electrons will fill the lowest energy levels. This is called the aufbau principle:
https://en.m.wikipedia.org/wiki/Aufbau_principle
So why don’t all the electrons just go into the lowest energy level and be done with it? Because electrons can’t all go into the lowest energy level. It’s a phenomenon known as Pauli’s exclusion principle:
https://en.m.wikipedia.org/wiki/Pauli_exclusion_principle
Electrons are fermions, and therefore only one electron is allowed to occupy a distinct quantum state. Based on these principles (and a few others relating to angular momentum), one can see that if an atom has 15 electrons, they will tend to occupy the 15 lowest energy orbital states. The valence orbitals are simply the highest of these low energy states that are occupied by electrons. The electrons occupying these valence orbitals are important because they are the ones that contribute most heavily to chemical bonding.
This is what I needed and I understand now, thank you.

I don't think this last answer is effective for someone who just sees the Bohr model for the first time ...

GC&C, have you seen the formula for the energies in the Bohr model ?

(formula picture: wikipedia | Bohr model | derivation )

The energies are negative (bound states -- zero or positive energy would mean a free electron, not in orbit) and there are an infinite number of them, but the energy is never infinite.

The Bohr model is restricted to looking at a single electron 'seeing' a positive charge at the origin. Meaning it applies reasonably well to an outer electron of an atom : an electron in the valence shell.
You haven't understood what I asked and I specifically wrote "## \textbf{ level } ##" which mathematically corresponds to ## n \in \mathbb{N} ## so this is just a memory refresh so you could recall about Bohr model .

By infinite energy levels I meant that I can have ## E_1 ## , ## E_2 ## , ... , ## E_\infty ## as the energy is quantified , I never said the energy can be infinite as if we have ## n=0 ## this situation corresponds to free electron not attached to any atom.

BvU
Homework Helper
2019 Award
I don't know, i'm learning chemistry for the first time that is why i'm asking
You haven't understood what I asked
I find comfort in knowing that I am not the only one
infinite energy levels
Google would say: "Did you mean 'an infinite number of energy levels' ?"
wrote "level " which mathematically corresponds to ## n \in \mathbb{N}##
Yes, well, this is a physics forum and an energy level corresponds to a real number (##\in \mathbb R##) times some unit of energy.
But don't let me distract you any further.