# 6.3 Development of quantum theory  (Page 6/25)

 Page 6 / 25
$\begin{array}{c}\text{Δ}E={E}_{\text{final}}-{E}_{\text{initial}}\\ \\ \\ =-2.18\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{\text{f}}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{\text{i}}^{2}}\phantom{\rule{0.2em}{0ex}}\right)\phantom{\rule{0.2em}{0ex}}\text{J}\end{array}$

The values n f and n i are the final and initial energy states of the electron. [link] in the previous section of the chapter demonstrates calculations of such energy changes.

The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital    , which is distinct from an orbit , is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principle quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located.

Another quantum number is l , the angular momentum quantum number . It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l , l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell    . In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital.

Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n , p orbitals constitute a p subshell (e.g., 3 p if n = 3). The orbitals with l = 2 are called the d orbitals , followed by the f-, g-, and h- orbitals for l = 3, 4, 5, and there are higher values we will not consider.

There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n l – 1.

Consider the examples in [link] . The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1 s ( n = 1), 2 – 0 – 1 = 1 node for 2 s , and 3 – 0 – 1 = 2 nodes for the 3 s orbitals.

The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found.

If an electron has an angular momentum ( l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number , called m l, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of m l is zero. For p orbitals, l = 1, and m l can be equal to –1, 0, or +1. Generally speaking, m l can be equal to – l , –( l – 1), …, –1, 0, +1, …, ( l – 1), l . The total number of possible orbitals with the same value of l (a subshell) is 2 l + 1. Thus, there is one s -orbital for ml = 0 , there are three p -orbitals for ml = 1 , five d -orbitals for ml = 2 , seven f -orbitals for ml = 3 , and so forth. The principle quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in [link] .

#### Questions & Answers

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
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
hello am new here and I want to join you
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
where can I get the test bank or mcqs ? any idea ?
what are the types of intermolecular forces between organic compounds
Intermolecular forces exist between molecules of different units like van der waal force, hydrogen bonds
Salaudeen