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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 aromaticity
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aromaticity is a conjugated pi system specific to organic rings like benzene, which have an odd number of electron pairs within the system that allows for exceptional molecular stability
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sodium hydroxide (NaOH)
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is simply means a condensed water vapour
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a hydrocarbon contains 7.7 percent by mass of hydrogen and 92.3 percent by mass of carbon
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they are three 3
Adazion
TYPES OF COVALENT BOND-POLAR BOND-NON POLAR BOND-DOUBLE BOND-TRIPPLE BOND. There are three types of covalent bond depending upon the number of shared electron pairs. A covalent bond formed by the mutual sharing of one electron pair between two atoms is called a "Single Covalent bond.
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Atom is indivisible particles which take place in chemical reactions
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Zn(OH-)2
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A 45 ml of ph=1,hcl was reacted with a 55l ml of ph=13, naoh solution . what is the final ph
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coordination number is the number of atoms or ions immediately surrounding a central atom in a complex or crystal
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Antoine Lavoisier. Father of modern chemistry
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geometric isomerism are molecules that are locked into their spatial position with respect to one another due to a double Bond or ring structure
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Chromatography is a physical method of seperation where by mixtures that are in two phrases are separated
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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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