De Broglie Wavelength:
De Broglie Wavelength, proposed by Louis de Broglie in 1924, is a fundamental concept in quantum mechanics that connects the wave-like and particle-like behaviors of matter. This principle suggests that all particles, including electrons, atoms, and even macroscopic object...
The de Broglie wavelength is an important concept while studying quantum mechanics.
The wavelength (λ) that is associated with an object in relation to its momentum and
mass is known as the de Broglie wavelength. A particle’s de Broglie wavelength is
usually inversely proportional to its force.
What is De Broglie Wavelength?
According to Louis de Broglie, any particle which moves might very well behave like a
wave. Clinton Davisson and Lester Germer demonstrated this experiment in 1927.
Matter waves are waves that are related to the matter. De Broglie waves are another
name for them.
Except for photons, all particles have a different de Broglie wavelength formula. At non-
relativistic speeds, a particle's momentum is equal to its rest mass m multiplied by its
velocity v. The de Broglie wavelength is represented by λ.
de Broglie Waves
It is said that matter has a dual nature of wave particles. de Broglie waves, named after
the discoverer Louis de Broglie, is the property of a material object that varies in time or
space while behaving similarly to waves. It is also called matter-waves. It holds great
similarity to the dual nature of light, which behaves as a particle and wave that has been
proven experimentally
allows the crystal structure to be determined.
In a microscope, the size of the smallest features we can see is limited by the
wavelength used. With visible light, the smallest wavelength is 400 nm = 4 x 10 -7 m.
Typical electron microscopes use wavelengths 1000 times smaller and can be used to
study very fine details.
Thermal de Broglie Wavelength
The thermal de Broglie wavelength (λth) is approximately the average de Broglie
wavelength of the gas particles in an ideal gas at the specified temperature.
The thermal de Broglie wavelength is given by the expression:
λD = h / √ 2 π m kBT
where,
h = Planck constant
m = mass of a gas particle
kB = Boltzmann constant
T = temperature of the gas
, λD = λth = thermal de Broglie wavelength of the gas particles.
De Broglie Wavelength Formula: Explained With Derivation & Solved Examples
All matter has wave properties, and the observed wavelength of the matter is related to
its momentum. De Broglie proposed in his doctoral dissertation in 1924 that, like light,
electrons have both wave and particle properties. This assumption has also been
supported experimentally by the wave nature of electrons. Louis de Broglie, a physicist,
proposed that particles could have both wave and particle properties. According to the
De Broglie Wavelength Formula, wave-particle duality is a fundamental principle shared
by both radiation and matter, rather than an anomalous behaviour of light.
In this Physics article, you will learn about the De Broglie wavelength formula with its
derivation and solved examples.
De Broglie Wavelength Formula
According to de Broglie, the below equation is entirely general and applies to material
particles as well. As a result, the wavelength of a particle of mass m travelling at speed
is given by
The wavelength of the matter waves is referred to as the de Broglie wavelength.
Through Planck's constant, this equation connects the wave character ( wavelength)
and the particle character (momentum p).
Derivation of De Broglie Wavelength Formula or De Broglie Equation
We know from Einstein's mass-energy equivalence relation that,
E= mc2.......(1)
E = the particle's energy
m = particle's mass
c = the speed of light
Planck's theory states that each quantum of a wave has a discrete amount of energy
associated with it, and he provided the equation:
E=hf……..(2)
Where E is the particle's energy,
h= 6.62607 × 10-34 Js is Planck's constant, and f is frequency.
According to the De-Broglie hypothesis, Broglie's particles and waves behave similarly.
As a result, he equated the energy relation for particle and wave; equating equations (1)
and (2) yields:
mc2 = hf
Because particles do not travel at the speed of light in general, De Broglie substituted
the speed of light c for the velocity of a real particle v and obtained:
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