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Introduction
De Broglie wave, also known as matter wave, is characteristic of a material object’s behaviour or properties that changes in time or space in accordance with the mathematical equations that describe waves.
De Broglie waves explain the existence of subatomic particles at apparently unexpected locations because their waves penetrate limits in the same way that sound does. As a result, a heavy atomic nucleus might sometimes release a fragment of itself in a process known as alpha decay. As a particle, the fragment of the nucleus (alpha particle) lacks the energy to overcome the force barrier around the nucleus; nevertheless, as a wave, it can leakage through the barrier—that is, it has a certain probability of being found outside the nucleus.
De Broglie Wavelength
Louis de Broglie, a French physicist, proposed in 1924 that particles may have wave properties in addition to particle properties.
Three years later, the wave nature of electrons was discovered experimentally. On the other hand, objects we see or experience everyday, have a computed wavelength that is much smaller than that of electrons, so their wave properties have never been detected; and the characteristics of a material object that changes in time or space while behaving in a wave-like manner.
It is also known as matter-waves. Matter is believed to have a dual nature of wave-particles. It is very similar to the dual nature of light, which has been scientifically demonstrated to act as both a particle and a wave. As a result, De Broglie waves play a significant role only in the domain of subatomic particles.
De Broglie Equation
The De Broglie equation is most commonly used in defining the wave properties of matter. Or we can say it describes the wave nature of microscopic particles like electrons.
Moreover De Broglie suggests that any moving particle either microscopic or macroscopic will be associated with wave character, that is known as matter waves.
However, after sometime he comes off with the relation between velocity and momentum of particles using the wavelength, as sometimes particles behave as a wave.
Early it was not possible to prove both particle and wave nature of matter in a single experiment, because it is a fact that every single experiment is based on some principles and results must be related to the principle not only reflected in that experiment.
The particle that has very low mass and moves with the speed that is less than the speed of light behaves like a particle and wave both.
And to support this De Broglie derived an equation that relates the mass and wavelength of such smaller particles.
Derivation of De Broglie Equation
According to plank’s Quantum theory energy of an electromagnetic wave
E = hν =hc/λ —— eq 1
And according to Einstein energy of the particle is related to its mass and velocity
E = mc2 —— eq 2
If a smaller particle shows dual nature the energy will becomes the same and that is what De Broglie have done, he equated both of these energy equations for a particle moving with velocity v and have mass m
E = hc/λ =mv2
Now,
h/λ =mv
λ = h/mv
Where h = plank’s constant
This is the final equation given by Sir Broglie that relates the wavelength and momentum of a particle.
Applications of De Broglie Equation
- Because matter’s wave characteristics are only visible for extremely small objects, the de Broglie wavelength of a double-slit interference pattern is created with electrons as the source. De Broglie wavelength = 3.9 x 10-10 m for 10 eV electrons (the normal energy of an electron in an electron microscope).
This is similar to the distance between atoms. As a result, a crystal works as an electron diffraction grating. The crystal structure may be determined using the diffraction pattern.
- The wavelength used in a microscope limits the size of the smallest features that can be seen. The smallest wavelength in visible light is 400 nm = 4 x 10-7 m. Typical electron microscopes have wavelengths 1000 times smaller than visible light and may be used to study in very detail.
Conclusion
De Broglie waves explain the existence of subatomic particles at apparently unexpected locations because their waves penetrate limits in the same way that sound does. As a result, a heavy atomic nucleus might sometimes release a fragment of itself in a process known as alpha decay. The De Broglie equation is most commonly used in defining the wave properties of matter. Because matter’s wave characteristics are only visible for extremely small objects, the de Broglie wavelength of a double-slit interference pattern is created with electrons as the source.
