# 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:

so is HCl ionic compound
what is chemistry
where can I get the test bank or mcqs ? any idea ?
what are the types of intermolecular forces between organic compounds
What is chemistry
scientific study of structure of substances and of the way that they react with other substances
Haider
Thanks
khausar
welcome
Haider
Hi
khausar
hi 2
Haider
whr u from
Haider
are u writing GCE
Equin
Cameroon and u
Equin
Please what nuclear fusion and nuclear fission
في التسمية الشائعة للكيتونات يتم للمجموعة التي phenone إضافة لفظ تحتوي على الفينل
what is organic chemistry
what is thyroid land
what is density
A measure of the amount of matter contained by a given volume. The ratio of one quantity to that of another quantity.
Anoruo
mass divided by volume i.e. g/cm^3
Walter
A
lynda
what's molarity?
the concentration of a substance in solution, expressed as the number moles of solute per litre of solution
Anoruo
Please help me solve this question. A is a solution of 0.995mol/dm cube hydrochloride acid. B was prepared by diluting 10cm cube of a saturated solution of sodium trioxocarbonate (iv) to 100cm cube at room temperature. Assuming that 21.50cm cube of A reacted with 25cm cube of B. Calculate: i. Concentration of solution B in mol/dm cube. ii.Solubility of sodium trioxocarbonate (iv) at room temperature. Equation of the reaction: Na2Co3 +2HCL------> 2NaCL +H2O +CO2.
I don't know whether it's ok or not, but the answers I got are: I. 0.428 mol/dm^3 II. 4.54g per 100 g of water
Nazifa
In the first one, I first found out the amount of HCl in mol using moles=concentration x volume. Then I checked the ratio of Na2CO3 to HCl, which is 0.5 to 1. Therefore the moles of Na2CO3 will be half of HCl. Using the amount in moles and the volume as 25 cm^3, I reached my answer!
Nazifa
In the second one, it says that 10 cm^3 has saturated Na2CO3 solution. Using the concentration we found in previous answer, I found out the moles present in 10cm^3. After that, using mass= moles x RFM, I got it's mass. As for the mass of water, we know 1 cm^3 gives 1g, so 10 cm^3 gives 10g.....
Nazifa
Using solubility= mass of solute/mass of solvent x 100, we reach the answer.
Nazifa
Note: we will not use the volume of solution to be 100 cm^3, because then the solution will be dilute.
Nazifa
plz do correct me if I'm wrong!! ☺️
Nazifa
is like the answer is 900
lynda
how can I make citric acid crystals from lemon juice
Write the resonance hybrids of furan and thiophene
Hydrolysis of CH3CH2NO2 with 85% H2SO4 gives? 2/Acetaldehyde is oxidised with potassium dichromate and sulphuric acid gives 3/ When benzyl alcohol is oxidised with KMnO4, the product obtained ? 4/ Benzyl chloride is oxidised with KOH4, the 5/
Hydrolysis of CH3CH2NO2 with 85% H2SO4 gives?
Define reduction in term of loss or gain of oxygen or hydrogen give an example.
Aneela
CuO + Mg → Cu + MgO removing oxygen is reduction. here Mg is reducing agent(loss of electrons)
Haider
reduction >> reduc(+)ion mean (+)ion reduced mean electron gained by (+)ion (+)ion means H(+).
Haider
How what works