In mine textbook, it states that the maximum variety of electrons that deserve to fit in any kind of given covering is given by 2n². This would average 2 electrons can fit in the first shell, 8 could fit in the second shell, 18 in the third shell, and 32 in the 4th shell.

However, i was previously taught that the maximum variety of electrons in the an initial orbital is 2, 8 in the second orbital, 8 in the third shell, 18 in the 4th orbital, 18 in the 5th orbital, 32 in the sixth orbital. I am fairly sure that orbitals and shells are the exact same thing.

Which of this two methods is correct and also should be used to uncover the variety of electrons in one orbital?

I to be in high institution so please shot to leveling your answer and also use relatively basic terms.

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Shells and orbitals room not the same. In terms of quantum numbers, electrons in different shells will have different values of primary quantum number n.

To answer your question...

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

The 1s orbital

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

The 2s orbitalThe 2p orbitals

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

The 3s orbitalThe 3p orbitalsThe 3d orbitals

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

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

So one more kind of orbitals (s, p, d, f) becomes accessible as we go come a shell with higher n. The number in former 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 various kinds of orbitalsEach type of orbital has a various \"shape\", as you deserve to see ~ above the snapshot below. You can additionally see that:

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

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Each orbital deserve to hold two electrons. One spin-up and also one spin-down. This way that the 1s, 2s, 3s, 4s, etc., have the right to each organize two electrons because they each have only one orbital.

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

Thus, to discover the variety of electrons feasible per shell

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

The 1s orbital

An s-orbital stop 2 electrons. For this reason n=1 shell deserve to hold 2 electrons.

The n=2 (second) covering has:

The 2s orbitalThe 2p orbitals

s-orbitals can hold 2 electrons, the p-orbitals can hold 6 electrons. Thus, the second shell can 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 have the right to hold 6, and d-orbitals have the right to hold 10, because that a total of 18 electrons.

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

There\"s vital distinction in between \"the variety of electrons feasible in a shell\" and \"the number of valence electrons possible for a period of elements\".

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There\"s space for $18 \\texte^-$ in the 3rd shell: $3s + 3p + 3d = 2 + 6 + 10 = 18$, however, facets 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 obtain to elements from the 4th period - ie. Facets from the 3rd period don\"t to fill the third shell.

The orbitals room filled so the the people of lowest power are filled first. The power is about like this: