Question

what do you mean by dual nature of matter? show that de Broglie's wave length is inversly proportional to the velocity of the particle

Answer 1

particle and the wave nature. , de Broglie wavelength is = h/ √2mQv

Answer 2

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According to the concept of De Broglie's concept of matter shows their two properties according to the conditions :

As Wave ( in state of moving ).

As Praticle ( in state of rest ) .

⠀⠀⠀⠀⠀━ So , that's why Matter has dual nature .

⠀⠀⠀⠀▪︎ According to the De Broglie's equation suggests that the wave length of any object is inversely proportional to its momentum ( or product of mass & Velocity )

Therefore,

Representation in Mathematical Eq. :

$\qquad \dag\:\:\bigg\lgroup \sf{ \lambda \:= \dfrac{h}{mv}}\bigg\rgroup$

⠀⠀⠀⠀Here , h is the Plank's Quantity , mv is the momentum ( product of mass(m) and Velocity(v) is known as momentum ) & $\bf \lambda$ is the wavelength.

Now , We can clearly see that ,

⠀⠀⠀⠀▪︎ Wave length is inversely proportional to the velocity of the particle.

$\qquad \dag\:\:\bigg\lgroup \sf{ \lambda \propto \dfrac{1}{v}}\bigg\rgroup$

⠀⠀⠀⠀Here , $\bf \lambda$ is the wavelength and v is the velocity.

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⠀⠀⠀⠀⠀More To Know about Dual nature of Matter :

It was proposed by De Broglie .

It was proposed in 1923

It was verified by Davisson & Gerber by the Diffraction.

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