# 6.3 Development of quantum theory

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By the end of this section, you will be able to:
• Extend the concept of wave–particle duality that was observed in electromagnetic radiation to matter as well
• Understand the general idea of the quantum mechanical description of electrons in an atom, and that it uses the notion of three-dimensional wave functions, or orbitals, that define the distribution of probability to find an electron in a particular part of space
• List and describe traits of the four quantum numbers that form the basis for completely specifying the state of an electron in an atom

Bohr’s model explained the experimental data for the hydrogen atom and was widely accepted, but it also raised many questions. Why did electrons orbit at only fixed distances defined by a single quantum number n = 1, 2, 3, and so on, but never in between? Why did the model work so well describing hydrogen and one-electron ions, but could not correctly predict the emission spectrum for helium or any larger atoms? To answer these questions, scientists needed to completely revise the way they thought about matter.

## Behavior in the microscopic world

We know how matter behaves in the macroscopic world—objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle: It will continue in a straight line unless it collides with another ball or the table cushion, or is acted on by some other force (such as friction). The ball has a well-defined position and velocity (or a well-defined momentum, p = mv, defined by mass m and velocity v ) at any given moment. In other words, the ball is moving in a classical trajectory. This is the typical behavior of a classical object.

When waves interact with each other, they show interference patterns that are not displayed by macroscopic particles such as the billiard ball. For example, interacting waves on the surface of water can produce interference patters similar to those shown on [link] . This is a case of wave behavior on the macroscopic scale, and it is clear that particles and waves are very different phenomena in the macroscopic realm.

As technological improvements allowed scientists to probe the microscopic world in greater detail, it became increasingly clear by the 1920s that very small pieces of matter follow a different set of rules from those we observe for large objects. The unquestionable separation of waves and particles was no longer the case for the microscopic world.

One of the first people to pay attention to the special behavior of the microscopic world was Louis de Broglie . He asked the question: If electromagnetic radiation can have particle-like character, can electrons and other submicroscopic particles exhibit wavelike character? In his 1925 doctoral dissertation, de Broglie extended the wave–particle duality of light that Einstein used to resolve the photoelectric-effect paradox to material particles. He predicted that a particle with mass m and velocity v (that is, with linear momentum p ) should also exhibit the behavior of a wave with a wavelength value λ , given by this expression in which h is the familiar Planck’s constant:

what is hybridization
the mixing of atomic orbitals to form molecular of similar energy called hybrid orbitals
Cffrrcvccgg
who are the alchemist?
alchemy science of transmutation. typically it is aim at tranforming lead to or other base metals to gold and the creation of the philosophers stone which in reality isn't a stone it's something priceless something we all need for coming times. don't be fooled
Kendrick
read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
Kendrick
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
Michael
Wow!
mendie
What's the mass number of carbon
Akinbola
mass number of carbon is 12.
Nnenna
wat d atomic number of oxygen
safiya
atomic number of oxygen is 8
Nnenna
which quantum number divides shell into orbitals?
azimuthal
Emmanuel
hi
Charlie
azimuthal
reinhard
azimuthal
Charlie
what is atom
an atom is a smallest indivisible part of an element
Henry
an atom is the smallest part of an element that takes part in a chemical reaction
Nana
wat is neutralization
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
Santosh
explain buffer
Organic
buffer is a solution which resists changes in pH when acid or alkali added to it..
Santosh
hello, who is online
UTHMAN
buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
KAUSIK
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
KAUSIK
how to solve equation on this
what are the elent of ionic and covalent bonding
Princewill
what is gases
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
John
What is chemical bonding
John
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
What is mole
It's the unit of measurements used to express the amount of chemical substance.
Ozoaniehe
What is pressure
force over area
Jake
force applied per unit area
john
force applied per unit area
Prajapati
Why does carbonic acid don't react with metals
Why does carbonic acid don't react with metal
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object