# 6.3 Development of quantum theory  (Page 5/25)

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$\stackrel{^}{H}\psi =E\psi$

$\stackrel{^}{H}$ is the Hamiltonian operator, a set of mathematical operations representing the total energy of the quantum particle (such as an electron in an atom), ψ is the wavefunction of this particle that can be used to find the special distribution of the probability of finding the particle, and $E$ is the actual value of the total energy of the particle.

Schrödinger’s work, as well as that of Heisenberg and many other scientists following in their footsteps, is generally referred to as quantum mechanics    .

## Understanding quantum theory of electrons in atoms

The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding.

As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n . This number, n , is referred to as the principle quantum number. The principle quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level ( [link] ). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has.

This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom:

why is alkynes more reactive than alkenes and alkanes
Alkenes and alkynes are generally more reactive than alkanes due to the electron density available in their pi bonds.
Danny
What are molecules
a group of atoms bonded together, representing the smallest fundamental unit of a chemical compound that can take part in a chemical reaction
Danny
True
David
exactly
Harriet
true
lucy
were is ruth
Danny
Perfect
BISWAJIT
what is partial pressure law
what is the structural formular for 2,3-dimethylbutane?
name the following compound (COOH)2
Mercy
CH3-CH(CH3)-CH(CH3)-CH3 this is 2,3-dimethylbutane
galina
(COOH)2 is oxalic acid
thiru
what is chemistry
chemistry is the study of chemical reactions
lucy
Chemistry is the study of matter, its properties, how and why substances combine or separate to form other substances, and how substances interact with energy.
Danny
chemistry is the study of matter, it's properties and composition
alexandra
hello Lucy
alexandra
hello boris nice to meet u all
alexandra
hello
lucy
lucy were you from and what grade are you doing
Danny
am from Abuja and am in ss1
lucy
ss1 some one translate that for me we use grades in my country
Danny
lucy
okay am a chemistry and biology teacher from Zambia
Danny
should be grade 10 I think
alexandra
oh okay hello
lucy
thats good Mr mwanza
Harriet
Danny
GCE 12
Harriet
from where
Danny
lusaka
Harriet
text me on whats up
Danny
we help each other
Danny
yes sir
lucy
me ss2
Richard
so are a final year student
kabu
wow I didn't know it chat group
Emmanuel
hello..
Edgar
hello
edet
hi
Hey
Faith
I'm new here
edet
What is the chemical formula for alcohol? is the chemical formula for alcohol?
CH3CH2OH
Anupam
20 element are what element?
What is Chemistry?
thiru
Esther
studying about the rate of chemical is ?
thiru
Chemistry is the branch of sciences dealing with the composition of substances and their properties and reaction.
Jeremiah
chemical reaction is the process in which one or more chemical substances react with other chemical substance and converted one or more different substances.
Aisha
what is isotopy
Isotopy is one of two or more atoms having the same atomic numbers but different mass number.
Esther
Molar mass of Chlorine
molar mass of chlorine 35.5
lucy
what is chemistry
Molar mass of Chlorine atom
Sakyi
chem is the study of structure, properties of matter and changes that matter undergo
Sheila
m.m of Cl is 35.5
Sheila
what is an acid
example, HCl, H2SO4, HNO3
galina
an acid is a substance that dissolves in water to give hydrogen oins as the only negatively charged ions
Sheila
Galina is correct those are some examples of acids , others are ethanedioic acid, ethanoic acid , methanoic acid ma ans above is tha definition of an acid
Sheila
An acid is a substance with particular chemical properties including litmus red, neutralizing alkalis and dissolving some metals.
Esther
Shelia is also right 💯💯
Esther
what is hydrocarbon?
Edgar
is a group of carbon atoms that is bonded with an alkyl group eg methyl butane
Sheila
A hydrocarbon is a compound that contains only hydrogen and carbon atoms
martha
it means only carbon and hydrogen atoms are bonded..
Edgar
when ammonia and hydrogen ion bond together to form ammonium ion the bond formed is called
coordinate bond
Sheila
its called Dative covalent bond\ coordinate bond..
Favour
what are the factors affecting chemical equilibrium
Zee
what IS the meaning of esterification
it is converting a compound by replacing the hydrogen of an acid by an alkyl other organic group maybe caboxyl
Sheila
It is the method in which esters are produced. When alcohols are treated with carboxylic acids in presence of an acid,sweet smelling esters are produced.
BISWAJIT
thermodynamic first law
The first law of thermodynamics, also known as Law of Conservation of Energy, states that energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another
Alysa