<< Chapter < Page Chapter >> Page >
This diagram has an upward pointing arrow at the left which is labeled, “B subscript 0.” To the right, two spheres are shown. The first has a gray square at the top labeled, “N,” and a second gray square at the bottom labeled, “S.” A curved arrow is pointing right across the surface of the sphere and a gray arrow points upward through the center of the sphere. This sphere is labeled, “Spin plus one-half, spin-up.” The sphere just to the right has a gray square above it labeled, “S,” and a gray square below it labeled, “N.” This sphere has a curved arrow on its surface that is directed to the left and a gray arrow through the center of the sphere that points downward. This sphere is labeled, “Spin negative one-half spin-down.”
Electrons with spin values ± 1 2 in an external magnetic field.

[link] illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 1 2 spin quantum number and down (in the negative z direction) for the spin quantum number of 1 2 . A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron on [link] ) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with m s = 1 2 has a slightly lower energy in an external field in the positive z direction, and an electron with m s = 1 2 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting.

The pauli exclusion principle

An electron in an atom is completely described by four quantum numbers: n , l , m l , and m s . The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle    can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n , l , and m l ), but only if their spin quantum numbers m s have different values. Since the spin quantum number can only have two values ( ± 1 2 ) , no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.

The properties and meaning of the quantum numbers of electrons in atoms are briefly summarized in [link] .

Quantum Numbers, Their Properties, and Significance
Name Symbol Allowed values Physical meaning
principle quantum number n 1, 2, 3, 4, …. shell, the general region for the value of energy for an electron on the orbital
angular momentum or azimuthal quantum number l 0 ≤ l n – 1 subshell, the shape of the orbital
magnetic quantum number m l l m l l orientation of the orbital
spin quantum number m s 1 2 , 1 2 direction of the intrinsic quantum “spinning” of the electron

Working with shells and subshells

Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and m l for the orbitals in the n = 4 shell of an atom.

Solution

For n = 4, l can have values of 0, 1, 2, and 3. Thus, s , p , d , and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell), m l can only be 0. Thus, there is only one 4 s orbital. For l = 1 ( p -type orbitals), m can have values of –1, 0, +1, so we find three 4 p orbitals. For l = 2 ( d -type orbitals), m l can have values of –2, –1, 0, +1, +2, so we have five 4 d orbitals. When l = 3 ( f -type orbitals), m l can have values of –3, –2, –1, 0, +1, +2, +3, and we can have seven 4 f orbitals. Thus, we find a total of 16 orbitals in the n = 4 shell of an atom.

Check your learning

Identify the subshell in which electrons with the following quantum numbers are found: (a) n = 3, l = 1; (b) n = 5, l = 3; (c) n = 2, l = 0.

Answer:

(a) 3 p (b) 5 f (c) 2 s

Got questions? Get instant answers now!

Questions & Answers

what is hydrocarbon
Sensible Reply
this is an organic compound that consist of hydrogen and ox
Okafor
why is isotonic solution the as blood
Hawa Reply
Elaborate more pls
Adeyinka
could you rephrase the question please?
Elaine
what is hydrocarbon? pls
Sensible
Hydrocarbon are organic compound consisting of hydrogen and carbon atoms
Adeyinka
thanks
Sensible
why is electrolytes really active in water
Sensible
relationship between an orbit and a shell
Hawa Reply
relationship between orbit and a shell
Hawa
What a homogenous mixture
Allison Reply
these are mixture of same substance or particles
INETIABOR
they are mixture of same particles or substance
INETIABOR
Define homologous series
Chizoba Reply
it is an organic compound having the same chemical properties which differs in a successive member of CH4
Okafor
when iron is exposed to moisture and it rusts,the value of deltaG for the reaction is
Mary Reply
what is chemistry
Siyanbola Reply
it is a branch of science that deals with the mixture of chemicals and properties and uses of matter
Okafor
define aci according to Lewis
Ryhanna Reply
an acid is an electron pair acceptor according to lewis
Mary
What is a homogenous mixture
Allison
it is d mixture of d same substances or particle or compound
Okafor
the third ionization energy of aluminium
sanmi Reply
name the allotrope of carbon used in gas masks
Moses Reply
Discuss the synthesis of sucrose
Ojiya Reply
What is a glycoside and discuss the formation
Ojiya
explain the transitioning of glucose molecules from Fischer projection of glucose to the Haworth projection
Rosey Reply
what is quantum
hezekiah Reply
what are metalliod
hezekiah
Metalloids are substances having the characteristics of both metals and non-metals
Ngwesse
what is acid
Tobi
define acid according to lewis
Ryhanna
Acid is an electron acceptor
Adeyinka
Wat z quantum
Adeyinka
what is valency
odukoya Reply
The number of chemical bonds the atoms of a certain element can form.
kenicia
what is ionization energy?
Hussniz Reply
ionization energy is qualitatively defined as the minimum amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom, molecule or io
Tobi
Wow. Thumb 👍 up
Adeyinka
Very explanatory. Tanx
Adeyinka

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask