Question

DERIVE DEBROGLIE'S WAVELENGTH?

Answer 1

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(1.1)(1.1)E=mc2

with

EE = energy,mm = mass,cc = 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(1.2)(1.2)E=hν

with

EE = energy,hh = Plank's constant (6.62607 x 10-34 J s),νν= frequency

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

mc2=hν(1.3)(1.3)mc2=hν

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

mv2=hν(1.4)(1.4)mv2=hν

Through the equation λλ, de Broglie substituted v/λv/λfor νν and arrived at the final expression that relates wavelength and particle with speed.

mv2=hvλ(1.5)(1.5)mv2=hvλ

Hence

λ=hvmv2=hmv

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Answer 2

Explanation:

The de Broglie equation is an equation used to describe the wave properties of matter or particles.

de Broglie suggested that particles can exhibit properties of waves, and proved that every moving particle has a matter wave associated with it.

The wavelength of the wave depends on the mass and the velocity of the particle:

λ=h\mv,

where:λ is wavelength in m.

h =6.626×10−34J.

⋅

h is Planck's constant.

m is the mass of a particle in kg moving at a velocity

v in m/s.