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Question

Derive an expression for de Broglie wavelength of matter waves.

Solution
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de Broglie equated the energy equations of Planck (wave) and Einstein (particle).

E=hv (planck's relation)

E=mc2 (Einstein's mass - energy relation)

hv=mc2

hcλ=mc2 (or)

λ=hmc

For a particle moving with a velocity V,

λ=hmV=hp

where p=mV is the momentum of the particle.

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