# Understanding the concept of electron per shell

• Chemistry
• Chijioke
Chijioke
Homework Statement
Is shell number same as energy level
Relevant Equations
The maximum number of electron per shell is given as $$2(n^2)$$ where n is energy level number. And energy level is same as electron shell.
Looking at Cacium for th electron arrangements according to shell numbers is 2, 8,8,2 since Cacium have four shells.
Going by the formula
1st shell has:$$2n^2=2\times 1^2= 2 ~electrons$$
2nd shell has:$$2n^2=2\times 2^2= 8 ~electrons$$
3rd shell has:$$2n^2=2\times 3^2= 18 ~electrons$$
But unfortunately, Cacium has only twenty electrons.
I am thinking that the remaining 10 electrons should go into the 3rd energy level. But if that happens then Cacium would not be fit to still remain in period 4.
So why is the electron filling per shell for Cacium 2,8,8,2 and not 2,8,10 according to the formula giving for the maximum number of electron that can be found in a shell?
Thank you.

topsquark
The formula ##2n^2## gives the maximum number of electrons that can have the same principal quantum number ##n##, and given the name electron shell. However, for many-electron atoms, the energy does not only depend on ##n##. It turns out that electrons will be found in the ##n=4## shell before the ##n=3## shell is filled.

topsquark
Drakkith said:
That formula is for the maximum number of electrons per shell, not the actual. In calcium, the last two electrons go into the 4s orbital.
You reply makes it look like as if there two types of maximum electrons in a shell:
1. Maximum number of electron and
2. Actual maximum number of electrons.
Please I need to understand something here.

There aren't two maximums and I never said there were.

Chijioke said:
Please I need to understand something here.
I'm not sure what you are looking for. If I can put 20 apples in a box, but I only put 12 into the box, then there's the maximum number of apples per box and the actual.

The details of how electrons go into their orbitals is probably beyond the scope of your class.

## What is the maximum number of electrons that can occupy a single shell?

The maximum number of electrons that can occupy a single shell is determined by the formula 2n², where n is the principal quantum number (the shell number). For example, the first shell (n=1) can hold up to 2 electrons, the second shell (n=2) can hold up to 8 electrons, the third shell (n=3) can hold up to 18 electrons, and so on.

## How are electrons distributed in the shells of an atom?

Electrons are distributed in shells around the nucleus of an atom based on increasing energy levels. The distribution follows the Aufbau principle, which states that electrons fill the lowest energy levels first before moving to higher levels. This means that electrons will first fill the K shell (n=1), then the L shell (n=2), and so on.

## What is the significance of the principal quantum number?

The principal quantum number, denoted as n, signifies the main energy level or shell of an electron. It determines the distance of the shell from the nucleus and the energy associated with it. Higher principal quantum numbers correspond to shells that are further from the nucleus and have higher energy levels.

## Why do electron shells have different capacities?

Electron shells have different capacities because of the spatial distribution and energy levels of electrons. As the principal quantum number increases, the number of available orbitals in a shell increases, allowing for more electrons. The formula 2n² reflects this by accounting for the increasing number of orbitals and their capacity to hold electrons as the shell number increases.

## How do electron configurations affect chemical properties?

Electron configurations determine the arrangement of electrons in an atom's shells and subshells, influencing the atom's chemical properties and reactivity. Atoms with similar electron configurations, especially in their outermost shells (valence shells), exhibit similar chemical behavior. For example, elements in the same group of the periodic table have similar valence electron configurations, leading to similar chemical properties.

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