Derive an expression for de Broglie wavelength of matter waves.

Question

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Answer 1

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

$E = h v$ (planck's relation)

$E = m c^{2}$ (Einstein's mass - energy relation)

$h v = m c^{2}$

$\frac{h c}{λ} = m c^{2}$ (or)

$λ = \frac{h}{m c}$

For a particle moving with a velocity $V$ ,

$λ = \frac{h}{m V} = \frac{h}{p}$

where $p = m V$ is the momentum of the particle.

Answer 2

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

E = h v

(planck's relation)

E = m c^{2}

(Einstein's mass - energy relation)

h v = m c^{2}

\frac{h c}{λ} = m c^{2}

(or)

λ = \frac{h}{m c}

For a particle moving with a velocity

V

,

λ = \frac{h}{m V} = \frac{h}{p}

where

p = m V

is the momentum of the particle.