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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.

A photograph is shown of ripples in water. The ripples display an interference pattern with each other.
An interference pattern on the water surface is formed by interacting waves. The waves are caused by reflection of water from the rocks. (credit: modification of work by Sukanto Debnath)

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:

Questions & Answers

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
what is neclear energy
Moyosoreoluwa Reply
nuclear energy is the energy released during nuclear fission or fusion.especially when used to generate electricity
Inusah
How many processes to break down CARBON DIOXIDE into carbon and oxygen
Prabhakar 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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