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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 is an atom
Precious Reply
An atom is the smallest particle of an element which can take part in a chemical reaction..
how to find the rate of reaction?
what is isomerism ?
Lucky Reply
Formula for equilibrium
Danmori Reply
is it equilibrium constant
what us atomic of molecule
Imhologhomhe Reply
chemical formula for water
Muhammad Reply
what is elemental
Maryam Reply
what are the properties of pressure
How can water be turned to gas
what's a periodic table
Okiemute Reply
how does carbon catenate?
obuke Reply
condition in cracking from Diesel to petrol
Brient Reply
hey I don't understand anything in chemistry so I was wondering if you could help me
Ruth Reply
i also
I also
condition for cracking diesel to form kerosene
can you tell me
please let me know
what is periodic law
rotimi Reply
periodic law state that the physical and chemical properties of an element is the periodic function of their atomic number
how is valency calculated
Ashley Reply
How is velency calculated
Hi am Isaac, The number of electrons within the outer shell of the element determine its valency . To calculate the valency of an element(or molecule, for that matter), there are multiple methods. ... The valency of an atom is equal to the number of electrons in the outer shell if that number is fou
what is the oxidation number of this compound fecl2,fecl3,fe2o3
Asmau Reply
bonds formed in an endothermic reaction are weaker than the reactants but y r these compound stable at higher temperatures
zille Reply
what is a disproportionation reaction
Ogor Reply

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