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Learning objectives

By the end of this section, you will be able to:

  • 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 size 12{n} {} . 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, ... size 12{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.

A black and white portrait of Austrian physicist Wolfgang Pauli.
The Austrian physicist Wolfgang Pauli (1900–1958) played a major role in the development of quantum mechanics. He proposed the exclusion principle; hypothesized the existence of an important particle, called the neutrino, before it was directly observed; made fundamental contributions to several areas of theoretical physics; and influenced many students who went on to do important work of their own. (credit: Nobel Foundation, via Wikimedia Commons)

Let us examine how the exclusion principle applies to electrons in atoms. The quantum numbers involved were defined in Quantum Numbers and Rules as n, l, m l , s , and m s size 12{m rSub { size 8{s} } } {} . Since s size 12{s} {} is always 1 / 2 size 12{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 n , l , m l , m s . For example, the quantum numbers 2, 1, 0, 1 / 2 size 12{ left (2,` 1,` 0,` - 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 size 12{n} {} determines the energy state in the absence of a magnetic field. So we first choose n size 12{n} {} , and then we see how many electrons can be in this energy state or energy level. Consider the n = 1 size 12{n=1} {} level, for example. The only value l size 12{l} {} can have is 0 (see [link] for a list of possible values once n size 12{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 1, 0, 0, + 1/2 , and the other has 1, 0, 0, 1/2 . [link] illustrates that there can be one or two electrons having n = 1 size 12{n=1} {} , but not three.

Questions & Answers

What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
why god made humenity
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
when we face electric shock these elements work as a conductor that's why we got this shock
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
What is position?
Amoah Reply
What is law of gravition
sushil Reply
what is magnetism
Sandeep Reply
Practice Key Terms 4

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