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maximum number of electrons each shell
In my textbook it says that the maximum number of electrons that can fit in any given shell is given by 2n². Which would mean 2 electrons could
fit in the first shell, 8 could fit in the second shell, 18 in the third shell, and 32 in the fourth shell. However, I was previously taught that the
maximum number of electrons in the first orbit is 2, 8 in the second orbit, 8 in the third shell, 18 in the fourth orbit, 18 in the fifth orbit, 32 in the
sixth orbit. I am fairly sure that orbits and shells are the same thing.
Which of these 2 methods is correct and should be used to find the number of electrons in an orbit?
I am in high school so please try to simplify your answer and use fairly basic terms.
physical-chemistry
electrons
electronic-configuration
edited Jul 16 at 17:31
ron
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asked Feb 20 at 4:13
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user3034084
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2 Answers
Shells and orbitals are not the same thing. In terms of quantum numbers, electrons in different shells
will have different values of principal quantum number n.
To answer your question...
In the first shell (n=1), we have:
The 1s orbital
In the second shell (n=2), we have:
The 2s orbital
The 2p orbitals
In the third shell (n=3), we have:
The 3s orbital
The 3p orbitals
The 3d orbitals
In the fourth shell (n=4), we have:
The 4s orbital
The 4p orbitals
The 4d orbitals
The 4f orbitals
So another kind of orbitals (s, p, d, f) becomes available as we go to a shell with higher n. The
number in front of the letter signifies which shell the orbital(s) are in. So the 7s orbital will be in the
7th shell.
Now for the different kinds of orbitals Each kind of orbital has a different "shape", as you can see
on the picture below. You can also see that:
The s-kind has only one orbital
The p-kind has three orbitals
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physical chemistry - maximum number of electrons each shell - Chemistry Stack Exchange
9/8/14 10:41 AM
The d-kind has five orbitals
The f-kind has seven orbitals
Each orbital can hold two electrons. One spin-up and one spin-down. This means that the 1s, 2s, 3s,
4s, etc., can each hold two electrons, because they each have only one orbital.
The 2p, 3p, 4p, etc., can each hold six electrons, because they each have three orbitals, that can
hold two electrons each (3*2=6).
The 3d, 4d etc., can each hold ten electrons, because they each have five orbitals, and each orbital
can hold two electrons (5*2=10).
Thus, to find the number of electrons possible per shell
First we look at the n=1 shell (the first shell). It has:
The 1s orbital
An s-orbital holds 2 electrons. Thus n=1 shell can hold two electrons.
The n=2 (second) shell has:
The 2s orbital
The 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) shell has:
The 3s orbital
The 3p orbitals
The 3d orbitals
s-orbitals can hold 2 electrons, p-orbitals can hold 6, and d-orbitals can hold 10, for a total of 18
electrons.
Therefore, the formula 2n 2 holds! What is the difference between your two methods?
There's an important distinction between "the number of electrons possible in a shell" and "the
number of valence electrons possible for a period of elements".
There's space for 18e − 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 because the 3d -orbitals aren't filled until
we get to elements from the 4th period - ie. elements from the 3rd period don't fill the 3rd shell.
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physical chemistry - maximum number of electrons each shell - Chemistry Stack Exchange
9/8/14 10:41 AM
The orbitals are filled so that the ones of lowest energy are filled first. The energy is roughly like this:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s
An easy way to visualise this is like this:
edited Feb 20 at 14:08
answered Feb 20 at 12:06
Brian
1,492
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15
The pattern of maximum possible electrons = 2n 2 is correct.
Also note that Brian's answer is good and takes a different approach.
Have you learned about quantum numbers yet?
If not...
Each shell (or energy level) has some number of subshells, which describe the types of atomic
orbitals available to electrons in that subshell. For example, the s subshell of any energy level
consists of spherical orbitals. The p subshell has dumbbell-shaped orbitals. The orbital shapes start
to get weird after that. Each subshell contains a specified number of orbitals, and each orbital can
hold two electrons. The types of subshells available to a shell and the number of orbitals in each
subshell are mathematically defined by quantum numbers. Quantum numbers are parameters in the
wave equation that describes each electron. The Pauli Exclusion Principle states that no two
electrons in the same atom can have the exact same set of quantum numbers. A more thorough
explanation using quantum numbers can be found below. However, the outcome is the following:
The subshells are as follows:
The s subshell has one orbital for a total of 2 electrons
The p subshell has three orbitals for a total of 6 electrons
The d subshell has five orbitals for a total of 10 electrons
The f subshell has seven orbitals for a total of 14 electrons
The g subshell has nine orbitals for a total of 18 electrons
The h subshell has eleven orbitals for a total of 22 electrons
etc.
Each energy level (shell) has more subshells available to it:
The first shell only has the s subshell
⟹ 2 electrons
The second shell has the s and p subshells ⟹ 2 + 6 = 8 electrons
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physical chemistry - maximum number of electrons each shell - Chemistry Stack Exchange
9/8/14 10:41 AM
The second shell has the s and p subshells
⟹ 2 + 6 = 8 electrons
The third shell has the s, p , and d subshells ⟹ 2 + 6 + 10 = 18 electrons
The fourth shell has the s , p, d, and f subshells ⟹ 2 + 6 + 10 + 14 = 32 electrons
The fifth shell has the s, p, d , f , and g subshells ⟹ 2 + 6 + 10 + 14 + 18 = 50 electrons
The sixth shell has the s, p, d , f , g , and h subshells ⟹ 2 + 6 + 10 + 14 + 18 + 22 = 72
electrons
The pattern is thus: 2, 8, 18, 32, 50, 72, . . . or 2n 2
In practice, no known atoms have electrons in the g or
model predicts their existence.
h subshells, but the quantum mechanical
Using quantum numbers to explain why the shells have the subshells they do and why the
subshells have the number of orbitals they do.
Electrons in atoms are defined by 4 quantum numbers. The Pauli Exclusin Principle means that no
two electrons can share the same quantum numbers.
The quantum numbers:
n, the principle quantum number defines the shell. The values of n are integers: n = 1, 2, 3, . . .
ℓ, the orbital angular momentum quantum number defines the subshell. This quantum number
defines the shape of the orbitals (probability densities) that the electrons reside in. The values of
ℓ are integers dependent on the value of n: ℓ = 0, 1, 2, . . . , n − 1
mℓ , the magnetic quantum number defines the orientation of the orbital in space. This quantum
number also determines the number of orbitals per subshell. The values of mℓ are integers and
depend on the value of ℓ: mℓ = −ℓ, . . . , −1, 0, 1, . . . , +ℓ
ms , the spin angular momentum quantum number defines the spin state of each electron. Since
there are only two allowed values of spin, thus there can only be two electrons per orbital. The
1
values of ms are ms = ±
2
For the first shell, n = 1 , so only one value of ℓ is allowed: ℓ = 0 , which is the s subshell. For
ℓ = 0 only mℓ = 0 is allowed. Thus the s subshell has only 1 orbital. The first shell has 1 subshell,
which has 1 orbital with 2 electrons total.
For the second shell, n = 2 , so the allowed values of ℓ are: ℓ = 0 , which is the s subshell, and
ℓ = 1 , which is the p subshell. For ℓ = 1 , mℓ has three possible values: mℓ = −1, 0, +1 . Thus
the p subshell has three orbitals. The second shell has 2 subshells: the s subshell, which has 1
orbital with 2 electrons, and the p subshell, which has 3 orbitals with 6 electrons, for a total of 4
orbitals and 8 electrons.
For the third shell, n = 3 , so the allowed values of ℓ are: ℓ = 0 , which is the s subshell, ℓ = 1 ,
which is the p subshell, and ℓ = 2 , which is the d subshell. For ℓ = 2 , mℓ has five possible values:
mℓ = −2, −1, 0, +1, +2 . Thus the d subshell has five orbitals. The third shell has 3 subshells: the s
subshell, which has 1 orbital with 2 electrons, the p subshell, which has 3 orbitals with 6 electrons,
and the d subshell, which has 5 orbitals with 10 electrons, for a total of 9 orbitals and 18 electrons.
For the fourth shell, n = 4 , so the allowed values of ℓ are: ℓ = 0 , which is the s subshell, ℓ = 1 ,
which is the p subshell, ℓ = 2 , which is the d subshell, and ℓ = 3 , which is the f subshell. For
ℓ = 3 , mℓ has seven possible values: mℓ = −3, −2, −1, 0, +1, +2, −3 . Thus the f subshell has
seven orbitals. The fourth shell has 4 subshells: the s subshell, which has 1 orbital with 2 electrons,
the p subshell, which has 3 orbitals with 6 electrons, the d subshell, which has 5 orbitals with 10
electrons, and the f subshell, which has 7 orbitals with 14 electrons, for a total of 16 orbitals and 32
electrons.
edited Feb 20 at 14:10
answered Feb 20 at 12:06
Ben Norris
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16
51
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