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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 a mole?
Henry Reply
pls give me 3 type of transition metal
Destiny Reply
Copper, Scandium, Vanadium, Iron, Chromium, Cobalt
Jumaane-Kalif
ion zinc hydrogen
Abdul
that is not true
Jumaane-Kalif
stop posting foolishness
Jumaane-Kalif
how do I name compounds
Stanley Reply
depends on the compound. as you may know there's transition metal compounds and there's organic compounds and so on and so forth.
Jumaane-Kalif
what is electricity
Lorrita Reply
electricity refers to the flow electrons
John
Hi. please can you tell me more on chemical equation
Gift Reply
When 1 or 2 chemicals react, they rearrange their atomic composition forming new compounds. The total mass before and after is the same/ constant. Chemical equations of same reactants react in same ratios e.g. 1 Na ion reacts with 1 water molecule or a multipier like 1 mole of Na ions react with 1
Abdelkarim
Mole of water molecules. In that example we multipied by 6.02*10^23 or avogadro constant (L). Or 2 Na+ ions with two water molecules. The arrow means '' to form '' Some times conditions or reactants are written above the arrow like H+ or enzyme or temper, sometimes physical states are written
Abdelkarim
Beside the chemical Aqueous (aq) which means solute dissolved on water. Solid (s) etc Some chemical equations are written next to it ΔH= # which means enthalpy change which describes if the reaction is endothermic (+) or exothermic (-).
Abdelkarim
Some are reversible and have half double arrow sign.
Abdelkarim
what is the meaning of atoma
Ibrahim Reply
what is theory
Michael Reply
what is chemical compound
Lorrita
A compound is the result of chemical bonding between 2 or more different elements.
Abdelkarim
Why is an atom electrically neutral?
Clara
difference between Amine and amide
Amadu Reply
what is the difference between alkanal and alkanone
Amadu
difference between alkanol and alkanal
Michael
whaatt
Saturday
you are not well at all
Ibrahim
is organic compounds used for drying agent
Olawale Reply
Sulfuric acid is used as a drying agent.
Abdelkarim
what is an atom
John Reply
An atom is the smallest part of an element, for instance gold atoms are the smallest part of gold that can enter a reaction. An atom must consist protons and electrons of equal number. You can think of those subatomic particles as spheres, but not orbiting randomly they move in specific way in
Abdelkarim
That was partially described mathematically. As a muslim, we believe that god created all matter from nothing. He is the Able, and only who can create matter in the begging in the big bang that was described in the Quran in chapter 17 verse 30, 1400 years ago, you can read it from internet.
Abdelkarim
what is electron affinity
John
do you have a private jet
Ibrahim
what is acid
Olubodun Reply
Proton donor (H+). Like in lemons, oranges and some medicines.
Abdelkarim
what is titration? and how can i get my readings?
favor Reply
what is electrolysis?
favor Reply
what is the formula you use when calculating for gas law?
favor
PV=nrt
Farid
electro-means electricity while lysis-means splitting up so electrolysis simply means splitting up by means of electric current
John
good day. how may I see previous question asked in this chat, please?
Asha
Asha, A person named Favor asked what is meant by the term electrolysis
John
what is gad law
Shampoo Reply
what is a sample
Dorcas Reply
According to google, a speciemen taken for specific testing or analysis.
Abdelkarim

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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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