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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

8 physical and chemical properties of aluminium
bolatito Reply
Question 91 in chapter 4 (finding the molarity of Calcium hydroxide), the answer given is 1.22 M and I have repeated the calculations numerous times and I keep getting 0.0122 M. Which is correct?
Hope Reply
what are the types of heat changes in chemical reaction
Chancha Reply
potassium is element number what, what is it symbol, what is it atomic weight, what it boiling point?
Vincent Reply
It is element number 19,symbol is K
Amha
atomic weight 39.0983g/mol boiling point 1047.0K
Johnson
I need 5 different and 5 similarities between compound and mixture
Mahmood Reply
Please send me answers
Mahmood
Please send me answers
Mahmood
Please send me answers
Mahmood
what is matter
Arinze Reply
Matter is anything that occupied space
Rasidi
matter is anything that has mass and occupies space
Johnson
matter is anything that has mass and volume.
rafaela
matter is any thing that can that has mass
samuel
a plot of the atomic radius against atomic number shows a periodic variation with group 1elements occupying the peaks and group 4 the troughs.plot the graph
Ngoline Reply
what is the periodic table all about
Godstime Reply
yeah
samuel
it's about predicting the different types of matter around us and organizing them in an elegant way
William
what is boyle law
Daniel Reply
the law states that at a constant absolute temperature the volume of a fixed of a gas is inversely proportional to the pressure of the gas...
Johnson
write short not on paper chromAtogphy
Ujunwa Reply
I am sorry, I don't understand the question. Are you referring to photospectometry, a machine that uses lightwaves to determine the chemical composition of a substance? Instead of the "coffee filter and solvent" method which is more crude, but simple enough to understand basic concepts.
Melissa
what is esterification?
Darey Reply
Esterification is the general name for a chemical reaction in which two reactants (typically an alcohol and an acid) form an ester(-COOR) as the reaction product....
Johnson
pls i dont know chemistry wat shall i do?
Chancha
Please...what do you mean by you don't know chemistry..can you explain further
Johnson
I am afraid you may end up injuring yourself working with these chemical processes with limited lab experience. Please be extremely careful. Research chem analysis, precedure and equipment.
Melissa
Pls can I be enlighten about boys law on chemistry
samuel
how we Learn full periodic table
muhammad Reply
how
Imran
Hello guys am new here my name is Angel from Nigeria how are u guys doing?
Angel Reply
Gud am from Nigeria too my name is sav
Michael
explain the atomic orbital
Masti Reply
2nacl➡️2na+cl2 2.58.5g 22.4l
suvarthavani 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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