Question

Derive Dr - broglie equation​

Answer 1

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Answer 2

$\huge\bold\red{Answer}$

De Broglie derived his equation using well established theories through the following series of substitutions:

De Broglie first used Einstein's famous equation relating matter and energy:

E=mc2(1)

with

E = energy,

m = mass,

c = speed of light

Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation:

E=hν(2)

with

E = energy,

h = Plank's constant (6.62607 x 10-34 J s),

ν = frequency

Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal:

mc2=hν(3)

Because real particles do not travel at the speed of light, De Broglie submitted velocity ( v ) for the speed of light ( c ).

mv2=hν(4)

Through the equation λ , de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particle with speed.

mv2=hvλ(5)

Hence

λ=hvmv2=hmv(6)

A majority of Wave-Particle Duality problems are simple plug and chug via Equation 6 with some variation of canceling out unit....