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H ^ ψ = E ψ

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 figure contains a central green sphere labeled “nucleus.” There is a plus sign in the middle of the sphere. This sphere is encircled by 3 concentric, evenly spaced rings. The first and closest to the center is labeled, “n equals 1.” The second ring is labeled, “n equals 2,” and the third ring is labeled, “n equals 3.” An arrow is drawn from the edge of the central sphere to the right extending out of the concentric rings. It is labeled, “increasing energy.”
Different shells are numbered by principle quantum numbers.

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:

Questions & Answers

what is an atom
Precious Reply
An atom is the smallest particle of an element which can take part in a chemical reaction..
olotu
hello
Karan
how to find the rate of reaction?
Karan
what is isomerism ?
Lucky Reply
Formula for equilibrium
Danmori Reply
is it equilibrium constant
olotu
Yes
Olatunde
yes
David
what us atomic of molecule
Imhologhomhe Reply
chemical formula for water
Muhammad Reply
H20
Samson
what is elemental
Maryam Reply
what are the properties of pressure
Maryam
How can water be turned to gas
VICTOR
what's a periodic table
Okiemute Reply
how does carbon catenate?
obuke Reply
condition in cracking from Diesel to petrol
Brient Reply
hey I don't understand anything in chemistry so I was wondering if you could help me
Ruth Reply
i also
Okikiola
I also
Brient
hello
Brient
condition for cracking diesel to form kerosene
Brient
Really?
Isa
yes
Brient
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Brient
please let me know
Brient
what is periodic law
rotimi Reply
periodic law state that the physical and chemical properties of an element is the periodic function of their atomic number
rotimi
how is valency calculated
Ashley Reply
How is velency calculated
Bankz
Hi am Isaac, The number of electrons within the outer shell of the element determine its valency . To calculate the valency of an element(or molecule, for that matter), there are multiple methods. ... The valency of an atom is equal to the number of electrons in the outer shell if that number is fou
YAKUBU
what is the oxidation number of this compound fecl2,fecl3,fe2o3
Asmau Reply
bonds formed in an endothermic reaction are weaker than the reactants but y r these compound stable at higher temperatures
zille Reply
what is a disproportionation reaction
Ogor Reply

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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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