<< Chapter < Page Chapter >> Page >
The figure here shows configuration of electrons. At the top, the key shows two purple balls, which depict electrons. The upward directed arrow on the first ball or electron shows its spin is plus one half, and the downward arrow on the second electron shows the opposite spin that is minus one half. Two other sections show the electronic configurations of electrons for two levels, n equal to one and n equal to two. One section shows the allowed configurations of the electron in the n is equal to one and two levels, and the second section for the configurations which are not allowed. In the allowed section, n is equal to two has three vacant shells and one electron in each of the outer two shells, one with spin up and one with spin down; and n is equal to one configuration has two shells containing one each spin up and spin down electron and the three other shells containing combinations of both spins each. For the not allowed section, n is equal to two have all vacant shells and n is equal to one have unevenly balanced electrons in its shells.
The Pauli exclusion principle explains why some configurations of electrons are allowed while others are not. Since electrons cannot have the same set of quantum numbers, a maximum of two can be in the n = 1 size 12{n=1} {} level, and a third electron must reside in the higher-energy n = 2 size 12{n=2} {} level. If there are two electrons in the n = 1 size 12{n=1} {} level, their spins must be in opposite directions. (More precisely, their spin projections must differ.)

Shells and subshells

Because of the Pauli exclusion principle, only hydrogen and helium can have all of their electrons in the n = 1 size 12{n=1} {} state. Lithium (see the periodic table) has three electrons, and so one must be in the n = 2 size 12{n=2} {} level. This leads to the concept of shells and shell filling. As we progress up in the number of electrons, we go from hydrogen to helium, lithium, beryllium, boron, and so on, and we see that there are limits to the number of electrons for each value of n size 12{n} {} . Higher values of the shell n size 12{n} {} correspond to higher energies, and they can allow more electrons because of the various combinations of l , m l size 12{l, m rSub { size 8{l} } } {} , and m s size 12{m rSub { size 8{s} } } {} that are possible. Each value of the principal quantum number n size 12{n} {} thus corresponds to an atomic shell    into which a limited number of electrons can go. Shells and the number of electrons in them determine the physical and chemical properties of atoms, since it is the outermost electrons that interact most with anything outside the atom.

The probability clouds of electrons with the lowest value of l size 12{l} {} are closest to the nucleus and, thus, more tightly bound. Thus when shells fill, they start with l = 0 size 12{l=0} {} , progress to l = 1 size 12{l=1} {} , and so on. Each value of l size 12{l} {} thus corresponds to a subshell    .

The table given below lists symbols traditionally used to denote shells and subshells.

Shell and subshell symbols
Shell Subshell
n size 12{n} {} l size 12{l} {} Symbol
1 0 s size 12{s} {}
2 1 p size 12{p} {}
3 2 d size 12{d} {}
4 3 f size 12{f} {}
5 4 g size 12{g} {}
5 h size 12{h} {}
6 It is unusual to deal with subshells having l greater than 6, but when encountered, they continue to be labeled in alphabetical order. i size 12{i} {}

To denote shells and subshells, we write nl size 12{ ital "nl"} {} with a number for n size 12{n} {} and a letter for l size 12{l} {} . For example, an electron in the n = 1 size 12{n=1} {} state must have l = 0 size 12{l=1} {} , and it is denoted as a 1 s size 12{1s} {} electron. Two electrons in the n = 1 size 12{n=1} {} state is denoted as 1 s 2 size 12{1s rSup { size 8{2} } } {} . Another example is an electron in the n = 2 size 12{n=2} {} state with l = 1 size 12{l=1} {} , written as 2 p size 12{2p} {} . The case of three electrons with these quantum numbers is written 2 p 3 size 12{2p rSup { size 8{3} } } {} . This notation, called spectroscopic notation, is generalized as shown in [link] .

Diagram illustrating the components of the expression 2 times p to the third power, where 2 is the pricncipal quantum number n, p is the angular momentum quantum number, represented by a script letter l, and the exponent 3 is the number of electrons.

Counting the number of possible combinations of quantum numbers allowed by the exclusion principle, we can determine how many electrons it takes to fill each subshell and shell.

How many electrons can be in this shell?

List all the possible sets of quantum numbers for the n = 2 size 12{n=2} {} shell, and determine the number of electrons that can be in the shell and each of its subshells.

Strategy

Given n = 2 size 12{n=2} {} for the shell, the rules for quantum numbers limit l size 12{l} {} to be 0 or 1. The shell therefore has two subshells, labeled 2 s size 12{2s} {} and 2 p size 12{2p} {} . Since the lowest l size 12{l} {} subshell fills first, we start with the 2 s size 12{2s} {} subshell possibilities and then proceed with the 2 p size 12{2p} {} subshell.

Solution

It is convenient to list the possible quantum numbers in a table, as shown below.

Image contains a table listing all possible quantum numbers for the n equals 2 shell. The table shows that there are a total of two electrons in the 2 s subshell and six electrons in the 2 p subshell, for a total of eight electrons in the shell.

Discussion

It is laborious to make a table like this every time we want to know how many electrons can be in a shell or subshell. There exist general rules that are easy to apply, as we shall now see.

Got questions? Get instant answers now!

Questions & Answers

material that allows electric current to pass through
Deng Reply
material which don't allow electric current is called
Deng
insulators
Covenant
how to study physic and understand
Ewa Reply
what is conservative force with examples
Moses
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
Practice Key Terms 4

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