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= Planck’s constant
p= linear momentum
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 Einstein’s 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 Broglie’s and
Einstein’s 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 = ½ m*v² and linear momentum,
p = m*v Click here to see
Calculating de Broglie wavelengths Click
here to see
References
