1. Home
  2. College physics
  3. Atomic physics
  4. The pauli exclusion principle

30.9 The pauli exclusion principle  (Page 3/11)

<< Chapter < Page
  College physics     Page 3 / 11
Chapter >> Page >

The number of electrons that can be in a subshell depends entirely on the value of l size 12{l} {} . Once l size 12{l} {} is known, there are a fixed number of values of m l size 12{m rSub { size 8{l} } } {} , each of which can have two values for m s size 12{m rSub { size 8{s} } } {} First, since m l size 12{m rSub { size 8{l} } } {} goes from − l size 12{ - l} {} to l in steps of 1, there are 2 l + 1 size 12{2l+1} {} possibilities. This number is multiplied by 2, since each electron can be spin up or spin down. Thus the maximum number of electrons that can be in a subshell is 2 2 l + 1 size 12{2 left (2l+1 right )} {} .

For example, the 2 s size 12{2s} {} subshell in [link] has a maximum of 2 electrons in it, since 2 2 l + 1 = 2 0 + 1 = 2 size 12{2 left (2l+1 right )=2 left (0+1 right )=2} {} for this subshell. Similarly, the 2 p size 12{2p} {} subshell has a maximum of 6 electrons, since 2 2 l + 1 = 2 2 + 1 = 6 size 12{2 left (2l+1 right )=2 left (2+1 right )=6} {} . For a shell, the maximum number is the sum of what can fit in the subshells. Some algebra shows that the maximum number of electrons that can be in a shell is 2 n 2 size 12{2n rSup { size 8{2} } } {} .

For example, for the first shell n = 1 size 12{n=1} {} , and so 2 n 2 = 2 size 12{2n rSup { size 8{2} } =2} {} . We have already seen that only two electrons can be in the n = 1 size 12{n=1} {} shell. Similarly, for the second shell, n = 2 size 12{n=2} {} , and so 2 n 2 = 8 size 12{2n rSup { size 8{2} } =8} {} . As found in [link] , the total number of electrons in the n = 2 size 12{n=2} {} shell is 8.

Subshells and totals for n = 3 size 12{n=3} {}

How many subshells are in the n = 3 size 12{n=3} {} shell? Identify each subshell, calculate the maximum number of electrons that will fit into each, and verify that the total is 2 n 2 size 12{2n rSup { size 8{2} } } {} .

Strategy

Subshells are determined by the value of l size 12{l} {} ; thus, we first determine which values of l size 12{ ital "ls"} {} are allowed, and then we apply the equation “maximum number of electrons that can be in a subshell = 2 2 l + 1 size 12{2 left (2l+1 right )} {} ” to find the number of electrons in each subshell.

Solution

Since n = 3 size 12{n=3} {} , we know that l can be 0, 1 , or 2 ; thus, there are three possible subshells. In standard notation, they are labeled the 3 s , 3 p , and 3 d size 12{3d} {} subshells. We have already seen that 2 electrons can be in an s state, and 6 in a p size 12{p} {} state, but let us use the equation “maximum number of electrons that can be in a subshell = 2 2 l + 1 size 12{2 left (2l+1 right )} {} ” to calculate the maximum number in each:

3 s has l = 0 ; thus, 2 2 l + 1 = 2 0 + 1 = 2 3 p has l = 1; thus, 2 2 l + 1 = 2 2 + 1 = 6 3 d has l = 2; thus, 2 2 l + 1 = 2 4 + 1 = 10 Total = 18 ( in the n = 3 shell )

The equation “maximum number of electrons that can be in a shell = 2 n 2 size 12{2n rSup { size 8{2} } } {} ” gives the maximum number in the n = 3 size 12{n=3} {} shell to be

Maximum number of electrons = 2 n 2 = 2 3 2 = 2 9 = 18.

Discussion

The total number of electrons in the three possible subshells is thus the same as the formula 2 n 2 size 12{2n rSup { size 8{2} } } {} . In standard (spectroscopic) notation, a filled n = 3 size 12{n=3} {} shell is denoted as 3 s 2 3 p 6 3 d 10 size 12{3s rSup { size 8{2} } 3p rSup { size 8{6} } 3d rSup { size 8{"10"} } } {} . Shells do not fill in a simple manner. Before the n = 3 size 12{n=3} {} shell is completely filled, for example, we begin to find electrons in the n = 4 size 12{n=4} {} shell.

Got questions? Get instant answers now!

Shell filling and the periodic table

[link] shows electron configurations for the first 20 elements in the periodic table, starting with hydrogen and its single electron and ending with calcium. The Pauli exclusion principle determines the maximum number of electrons allowed in each shell and subshell. But the order in which the shells and subshells are filled is complicated because of the large numbers of interactions between electrons.

Electron configurations of elements hydrogen through calcium
Element Number of electrons (Z) Ground state configuration
H 1 1 s 1 size 12{1s rSup { size 8{1} } } {}
He 2 1 s 2 size 12{1s rSup { size 8{2} } } {}
Li 3 1 s 2 size 12{1s rSup { size 8{2} } } {} 2 s 1 size 12{2s rSup { size 8{1} } } {}
Be 4 " 2 s 2 size 12{2s rSup { size 8{2} } } {}
B 5 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 1 size 12{2p rSup { size 8{1} } } {}
C 6 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 2 size 12{2p rSup { size 8{2} } } {}
N 7 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 3 size 12{2p rSup { size 8{3} } } {}
O 8 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 4 size 12{2p rSup { size 8{4} } } {}
F 9 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 5 size 12{2p rSup { size 8{5} } } {}
Ne 10 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 6 size 12{2p rSup { size 8{6} } } {}
Na 11 " 2 s 2 size 12{2s rSup { size 8{2} } } {} 2 p 6 size 12{2p rSup { size 8{6} } } {} 3 s 1 size 12{3s rSup { size 8{1} } } {}
Mg 12 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {}
Al 13 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 1 size 12{3p rSup { size 8{1} } } {}
Si 14 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 2 size 12{3p rSup { size 8{2} } } {}
P 15 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 3 size 12{3p rSup { size 8{3} } } {}
S 16 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 4 size 12{3p rSup { size 8{4} } } {}
Cl 17 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 5 size 12{3p rSup { size 8{5} } } {}
Ar 18 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 6 size 12{3p rSup { size 8{6} } } {}
K 19 " " " 3 s 2 size 12{3s rSup { size 8{2} } } {} 3 p 6 size 12{3p rSup { size 8{6} } } {} 4 s 1 size 12{4s rSup { size 8{1} } } {}
Ca 20 " " " " " 4 s 2 size 12{4s rSup { size 8{2} } } {}

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 4

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask