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:

>>>> λ = h/mv, where λ is wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v. de Broglie suggested that particles can exhibit properties of waves.

Explanation:

Louis de Broglie, in full Louis-Victor-Pierre-Raymond, 7e duc de Broglie, (born August 15, 1892, Dieppe, France—died March 19, 1987, Louveciennes), French physicist best known for his research on quantum theory and for predicting the wave nature of electrons. He was awarded the 1929 Nobel Prize for Physics.