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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's kinetic energy
Charity Reply
what is anion?
Hussniz Reply
an anion is a positively charge ion
ade
Thnkz
Hussniz
an anion is a negatively charged ion
Johnson
And anion is a negatively charged ion which move towards the anode which is positively charged.
Ngwesse
what is matter
Henry Reply
what is pressure
Henry
what is water?
Scarcies Reply
hydrogen gas burned into oxygen gas which forms a polar molecule, has a defenate shape volume but not shape. at 20 degrees Celsius exists as an aqueous solution. Is a solvent that dissolves many solutes into solution. And can act as an acid or a base.
David
HOW CAN ETHANOL BE PREPARED FORM CASSAVA.... (WITH EQUATION)
Obi Reply
by mixing
Henry
it is less dense than water
Erastus Reply
can cooking gas be durable in gallon. ..
mowete
no
PRINCESS
reason pls
mowete
What is happening
Oluchi Reply
Why does ice float on water?
Ngwesse
As it cools, olive oil slowly soldifies and froms a solid over a range of temperatures. Which best describes the solid?
Tammie Reply
definition of a sample
ashley Reply
a small part or quantity intended to show what the whole is like
Abdull
What does kj stand for ? or just k. example - 371K
Katr Reply
kilojoules or Kelvin
Annie
what is atom
divinegift Reply
atom is anything that has weight and can occupy space
Neutons
atom is the smallest particle of an element that can neitherbe divided nor destroyed
clin
atom is the smallest indivisible particle of an element.
Igbayima
atom is the smallest particle of an element that can neither be created,subdivided or destroyed
Gbolahan
All wrong
Gift
Do you know that atoms can further be devided
Gift
Go and read 📘 up Dalton atomic theory and who disproved.. Read 📘 up atomic theory
Gift
an atom is the smallest particle of an element that can take part in a chemical reaction
Anyebem
good@anyebem
Henry
what is anion?
Hussniz
what is a structure of atomic
Deren Reply
WATS atomic structure?
mowete
what is the meaning of intermolecular force
Eunice Reply
is the force of attraction that exist between two or more molecules
Johnson
What is a primary standard solution ?
Duval
a known solution
Fiko
Characteristic of a primary standard solution
Duval
pauli's exclusion is based on what?
avdhesh Reply
quantum theory
Charles
What is greatest modification made in dalton's atomic theory?
Ngwesse 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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