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Write down de Broglie’s relation and explain the terms therein.

Aniket Singh , 4 Months ago
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de Broglie's Relation:
The de Broglie relation connects the wavelength of a particle to its momentum and is given by:
λ=hp\lambda = \frac{h}{p}
Where:
• λ\lambda is the wavelength associated with the particle.
• hh is Planck's constant (approximately 6.626×10−34 J⋅s6.626 \times 10^{-34} \, \text{J} \cdot \text{s}).
• pp is the momentum of the particle.
Momentum (pp) of a particle is defined as the product of its mass (mm) and velocity (vv):
p=mvp = mv
Thus, de Broglie's relation can also be written as:
λ=hmv\lambda = \frac{h}{mv}
Explanation of the Terms:
• λ\lambda (Wavelength): The wavelength of the particle. According to de Broglie, every moving particle, whether it’s a photon or a material object like an electron, is associated with a wave-like behavior, and this wavelength is given by the de Broglie relation.
• hh (Planck's constant): This is a fundamental constant of nature that relates the energy of a photon to its frequency. It’s a very small number, reflecting the quantization of energy in quantum mechanics.
• mm (Mass of the particle): The mass of the particle moving with velocity vv. The mass determines the inertia of the particle, which affects its momentum.
• vv (Velocity of the particle): The speed of the particle in a given direction. This determines how fast the particle is moving and contributes to its momentum.
Concept:
The de Broglie wavelength suggests that particles, traditionally thought to behave only as particles, exhibit wave-like properties. This wave-particle duality is central to quantum mechanics, where particles like electrons can be treated as waves in certain circumstances, such as when analyzing electron diffraction patterns. The wavelength associated with a macroscopic object is generally extremely small and undetectable, but for very small particles like electrons, the wavelength can be significant.
In summary, de Broglie's relation reveals the dual nature of matter, allowing particles to exhibit both particle-like and wave-like properties depending on the context.

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