In my textbook, it states that the maximum number of electrons that have the right to fit in any given shell is provided by 2n². This would average 2 electrons might fit in the first shell, 8 could fit in the 2nd shell, 18 in the 3rd shell, and 32 in the 4th shell.

However, ns was previously taught the the maximum number of electrons in the first orbital is 2, 8 in the 2nd orbital, 8 in the third shell, 18 in the fourth orbital, 18 in the fifth orbital, 32 in the 6th orbital. I am reasonably sure the orbitals and also shells space the very same thing.

Which of these two techniques is correct and should be provided to uncover the variety of electrons in an orbital?

I to be in high school so please try to simplify your answer and use relatively basic terms.

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Shells and also orbitals space not the same. In terms of quantum numbers, electron in different shells will certainly have different values of principal quantum number n.

To answer her question...

In the an initial shell (n=1), we have:

The 1s orbital

In the second shell (n=2), we have:

The 2s orbitalThe 2p orbitals

In the 3rd shell (n=3), us have:

The 3s orbitalThe 3p orbitalsThe 3d orbitals

In the fourth shell (n=4), us have:

The 4s orbitalThe 4p orbitalsThe 4d orbitalsThe 4f orbitals

So another kind the orbitals (s, p, d, f) becomes available as we go come a covering with greater n. The number in prior of the letter signifies which covering the orbital(s) are in. For this reason the 7s orbital will certainly be in the 7th shell.

Now because that the different kinds of orbitalsEach sort of orbital has actually a different "shape", together you deserve to see ~ above the snapshot below. Friend can additionally see that:

The s-kind has only one orbitalThe p-kind has actually three orbitalsThe d-kind has 5 orbitalsThe f-kind has seven orbitals

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Each orbital can hold two electrons. One spin-up and one spin-down. This method that the 1s, 2s, 3s, 4s, etc., have the right to each host two electrons because they each have actually only one orbital.

The 2p, 3p, 4p, etc., can each host six electrons due to the fact that they each have three orbitals, that can hold two electrons every (3*2=6).

The 3d, 4d etc., deserve to each organize ten electrons, since they each have five orbitals, and each orbital can hold two electron (5*2=10).

Thus, to discover the number of electrons feasible per shell

First, we look in ~ the n=1 covering (the very first shell). That has:

The 1s orbital

An s-orbital holds 2 electrons. Therefore n=1 shell have the right to hold two electrons.

The n=2 (second) covering has:

The 2s orbitalThe 2p orbitals

s-orbitals have the right to hold 2 electrons, the p-orbitals deserve to hold 6 electrons. Thus, the second shell have the right to have 8 electrons.

The n=3 (third) covering has:

The 3s orbitalThe 3p orbitalsThe 3d orbitals

s-orbitals deserve to hold 2 electrons, p-orbitals can hold 6, and also d-orbitals can hold 10, because that a full of 18 electrons.

Therefore, the formula $2n^2$ holds! What is the difference in between your two methods?

There"s an essential distinction in between "the variety of electrons feasible in a shell" and also "the variety of valence electrons feasible for a duration of elements".

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There"s space for $18 \texte^-$ in the 3rd shell: $3s + 3p + 3d = 2 + 6 + 10 = 18$, however, elements in the 3rd period only have up to 8 valence electrons. This is due to the fact that the $3d$-orbitals aren"t filled until we acquire to facets from the 4th period - ie. Aspects from the third period don"t to fill the 3rd shell.

The orbitals space filled so the the people of lowest power are to fill first. The energy is around like this: