Question

de Broglie hypothesis

Answer 1

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According to de Broglie’s hypothesis, a moving material particle sometimes acts as a wave and sometimes as a particle; or a wave is associated with moving material particle, which controls the particle in every respect. The wave associated with moving particle is called matter wave or de Broglie wave, λ = h/(mv)

Where, m and v are the mass and velocity of the particle and h is Planck’s constant

According to Planck’s quantum theory, the energy of a photon of a radiation of frequency ν and wavelength λ is

E = hν

According to Einstein’s mass-energy relation,

E = mc2

From (i) and (ii), we obtain

hν = mc2

=> m = hv/c2

Since each photon moves with the same velocity c, the momentum of photon,

p = Mass × Velocity

So, p = (hv/c2)× c = hv/c = h/λ

That is,

λ = h/p

This equation is equally applicable to both the photons of radiation and other material particles.

Answer 2

Answer:

Explanation:

Considering Einstein's relationship of wavelength lambda to momentum p, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:

lambda = h / p

recall that h is Planck's constant

This wavelength is called the de Broglie wavelength. The reason he chose the momentum equation over the energy equation is that it was unclear, with matter, whether E should be total energy, kinetic energy, or total relativistic energy. For photons, they are all the same, but not so for matter.

Assuming the momentum relationship, however, allowed the derivation of a similar de Broglie relationship for frequency f using the kinetic energy Ek:

f = Ek / h