De Broglie Wavelength

Dr. Brown Chem 342

By: Jessica Luzetsky, Kirsten Wells, Aaron Jenkins


 

    The De Broglie Wavelength gives the wavelength of any particle traveling with linear momentum. It shows an inverse relationship between the linear momentum and wavelength distance (IE a particle with high momentum has a short wavelength). This also works to explain the macroscopic scale in that a macroscopic body has such a high momentum that the wavelength is so small it is undetectable and in turn explains why the wave-like properties cannot be observed.  
 

l=h/p      

h= Planckís constant

p= linear momentum

 

 

 

 

Classical vs. Quantum Approach
 

 

 

    In the Classical approach waves and particles are basically two different concepts. Huygens stated that light consists of waves that traveled in straight lines. This concept had flaws in that it could not explain all of lights characteristics. Newton then came up with the idea that light consist of small particles and this could explain lights behavior such as reflection. This concept was accepted for quite some time because it also explained refraction. However once the concept of diffraction came about in early 19th century this theory was questioned.   
 

    De Broglie then posed a theory, in 1924, claiming that all matter and not just light has wavelength nature. He used Einsteinís idea of Ephoton=hv and combined this idea of the momentum of a photon he was able to develop his hypothesis.  He believed that on the macro scale particles had such high momentum that their wavelengths could not be detected.  This theory was confirmed in electrons and electron diffraction. This posed valuable, in that it could explain all matter and not just light. Also, leading to the development that all matter possessed both wave and particle nature. 
 

    The idea of that all matter and radiation exhibits particle and wave characteristics is known as the wave-particle duality.  This can not be described using classical physics, however when we examine De Broglieís and Einsteinís ideas we have come to find that it is true.  Also, quantum says that energies of matter or radiation can not be varied where as classical incorrectly says that they can.  This is a base for quantum as we can say particles do not travel along finite paths but they are scattered through space like waves.

 

Click for more information on Louis De Broglie

 

Deriving λ=h/p from photoelectric effect and the relativistic equation Ephoton= c*p Click here to see

Deriving λ = h/(√(2mKE)) from KE = Ĺ m*v≤ and linear momentum, p = m*v  Click here to see

Calculating de Broglie wavelengths   Click here to see

 

 

References

 

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