# 6.3 Development of quantum theory  (Page 8/25)

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[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 $\frac{1}{2}$ spin quantum number and down (in the negative z direction) for the spin quantum number of $-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}.$ 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 ${m}_{s}=\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ has a slightly lower energy in an external field in the positive z direction, and an electron with ${m}_{s}=-\frac{1}{2}$ 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 $\left(±\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\right),$ 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 $\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.2em}{0ex}}-\frac{1}{2}$ 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.

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.

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

wat are hydrocarbon s
I think they are molecules that comprise only of hydrogen and carbon atoms ( they are organic if I'm not mistaken)
Mmathabo
am new here can I join
Yeko
give two properties of liquid
what is measurement
is the comparison of an unknown quantity with a fixed quantity of the same kind
How does an element differ from a compound? How are they similar?
an element is an indivisible particles that can take part in a reaction and consist of smaller or tiny particles i.e proton, neutrons and electron while a compound is when two or more element chemically combine together. They are similar when they are homogeneous compound. they take the same rxn.
Yusuf
an element is s chemically pure substance containing a particular type of atoms.. A COMPOUND is a substance containing atoms from different elements..
Inemesit
How to get the Lewis formula of SeCl+3
hi,I'm new here can I join the conversation
EZEA
what is the structural formula for starch
Starch is a mixture (of chemicals) of amylose and amylopectin. Both are macromolecules and polymers. You can search on wikipedia.
Abdelkarim
what is the roles of filter bed
Fathmat
what is the roles of Alu m
Fathmat
what is the roles of chlorine
Fathmat
Roles can be classified or correlate it to different areas: For example: Chlorine can be used in reactions (in industry) to manufacture HCl, which then can be used for other things. Or in swimming pools to kill bacteria. Or as a component in compounds with pharmaceutical roles (drugs). For Al:
Abdelkarim
Its dentisty value is suitable to be used in alloys (mixture of metals) in aircraft bodies. Also, Aluminium foils, Tin cans,.. Some of them are also in Al overhead cables in streets and long roads.
Abdelkarim
what is chemistry
Maxamed
what is the meaning of exceedingly
it is an adverb which means extremely
Rohini
what is atomic chemistry?
Lewis structure for no3
Lewis structure for no3
what is weak acid
It is an acid which partially ionises in water.
Abdelkarim
what is incandescence
Clifton
what makes it glow
Clifton
why is it red, irange and yellow in color
Clifton
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Aliyu
hello
Clifton
hi
Aliyu
too
Gillian
hello i am new here please i want to join this group
Paul
Hi, I'm also new here
Salaudeen
Hi
Keeya
hello guys !!
Sourav
what is pressure?
The force applied to suction Area of the body
Ahmed
Matter composed of exceedingly small paticle called atom.
Yushao
questions related to metals
occurrence and preparation of the representatives metals
Regina
list the 20, periodic table and their symbols
hydrogen:h helium;he lithium:l beryllium:be Boron:b Carbon;C Nitrogen:n Oxygen:O FLUORINE:f Neon:n Sodium:s Magnesium:mg Aluminum:a Silicon:s Phosphorus:p Sulphur:s Chlorine:c Argon;a Potassium:p Calcium:c
Benita
Hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium, silicon, phosphorus, sulphur, chlorine, argon, potassium, calcium
Cudjoe
what is a solute
Any substance that is disolved in a liqid solvent to create a solution
Fifa
sorry liquid
Fifa
it's a liquid substance
Fathmat
hello group
Ayomide
is the substance that dissolves in the solvent
Amos
so is HCl ionic compound
No, covalent compound ➡️ molecule. As both H and Cl are non-metals and and form covalent bind by sharing valence e-. But can fully ionice in water forming H+ (a proton, a reason for acidity) and Cl- (anion =Chloride) Hydrogen Chloride is a gas at room; Hydrochloric acid = HCl (aq), dissolved in w
Abdelkarim
Form covalenr bond*
Abdelkarim
The question marks are an emoji in the first sentence is an unread emoji. HCl Covalent compund -> molecule
Abdelkarim
Hi.
Queen
Hi
Calvin
Yh
Cudjoe
yes
Amos
what is chemistry
is the study of composition of substances and the way they behave under different conditions
Amos
how do calculate n1 though n6 any help on understanding the concept
Clifton
is the study of properties of matter and it's component
Grace