# 30.9 The pauli exclusion principle

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• Define the composition of an atom along with its electrons, neutrons, and protons.
• Explain the Pauli exclusion principle and its application to the atom.
• Specify the shell and subshell symbols and their positions.
• Define the position of electrons in different shells of an atom.
• State the position of each element in the periodic table according to shell filling.

## Multiple-electron atoms

All atoms except hydrogen are multiple-electron atoms. The physical and chemical properties of elements are directly related to the number of electrons a neutral atom has. The periodic table of the elements groups elements with similar properties into columns. This systematic organization is related to the number of electrons in a neutral atom, called the atomic number    , $Z$ . We shall see in this section that the exclusion principle is key to the underlying explanations, and that it applies far beyond the realm of atomic physics.

In 1925, the Austrian physicist Wolfgang Pauli (see [link] ) proposed the following rule: No two electrons can have the same set of quantum numbers. That is, no two electrons can be in the same state. This statement is known as the Pauli exclusion principle    , because it excludes electrons from being in the same state. The Pauli exclusion principle is extremely powerful and very broadly applicable. It applies to any identical particles with half-integral intrinsic spin—that is, having $s=1/2, 3/2, ...$ Thus no two electrons can have the same set of quantum numbers.

## Pauli exclusion principle

No two electrons can have the same set of quantum numbers. That is, no two electrons can be in the same state.

Let us examine how the exclusion principle applies to electrons in atoms. The quantum numbers involved were defined in Quantum Numbers and Rules as $\mathrm{n, l,}\phantom{\rule{0.25em}{0ex}}{m}_{l}\mathrm{, s}$ , and ${m}_{s}$ . Since $s$ is always $1/2$ for electrons, it is redundant to list $s$ , and so we omit it and specify the state of an electron by a set of four numbers $\left(n,\phantom{\rule{0.25em}{0ex}}l,\phantom{\rule{0.25em}{0ex}}{m}_{l},\phantom{\rule{0.25em}{0ex}}{m}_{s}\right)$ . For example, the quantum numbers $\left(2, 1, 0,\phantom{\rule{0.25em}{0ex}}-1/2\right)$ completely specify the state of an electron in an atom.

Since no two electrons can have the same set of quantum numbers, there are limits to how many of them can be in the same energy state. Note that $n$ determines the energy state in the absence of a magnetic field. So we first choose $n$ , and then we see how many electrons can be in this energy state or energy level. Consider the $n=1$ level, for example. The only value $l$ can have is 0 (see [link] for a list of possible values once $n$ is known), and thus ${m}_{l}$ can only be 0. The spin projection ${m}_{s}$ can be either $+1/2$ or $-1/2$ , and so there can be two electrons in the $n=1$ state. One has quantum numbers $\left(1, 0, 0,\phantom{\rule{0.25em}{0ex}}+1/2\right)$ , and the other has $\left(1, 0, 0,\phantom{\rule{0.25em}{0ex}}-1/2\right)$ . [link] illustrates that there can be one or two electrons having $n=1$ , but not three.

#### Questions & Answers

Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
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What is unit of watt?
Kulsum
watt is the unit of power
Rahul
p=f.v
Rahul
watt can also be expressed as Nm/s
Rahul
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
50 N... (50 *1.732)N
Sahim
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Is earth is an inertial frame?
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
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Irungu
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Sahim
Hey.. I've a question.
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
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Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
what is cesium atoms?
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
Chathu
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what are the solution to all the exercise..?
What is realm
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
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what is mean by Newtonian principle of Relativity? definition and explanation with example
what is art physics
I've been trying to download a good and comprehensive textbook for physics, pls can somebody help me out?
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c=1/c1+c2/1+c3 what is the answer
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smith
This may seem like a really stupid question, but is mechanical energy the same as potential energy? If not, what is the difference?
what is c=1\c1,c=2\c2,c=3\c3
Akinbulejo
mechanical energy is of two types 1: kinetic energy 2: potential energy,so, potential energy is actually the type of mechanical energy ,the mechanical due to position is designated as potential energy
Iram
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Nikki
Can someone possibly walk me through this problem? " A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgehammer. The hammer hits the spike with a speed of 65.0 m/s. If one-third Of the hammer's kinetic energy is converted to the internal energy of rhe hammer and spike.
Nikki
how much does the total internal energy increase
Nikki
you know the mass and the velocity of the hammer. therefore using the equation (mv^2)/2 you can find the kinetic energy. then take one third of this value and that will be your change in internal energy. here, the important thing is that spike is stationary so it does not contribute to initial Energ
Chathu
Thabk you! :)
Nikki