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:

• The De Broglie hypothesis proposes that all matter exhibits wave-like properties and relates the observed wavelength of matter to its momentum.
• After Albert Einstein's photon theory became accepted, the question became whether this was true only for light or whether material objects also exhibited wave-like behavior

For a photon having wave nature ,From planks equation

E=h×frequency

=hc/λ

For a photon having particle nature, From Einstein energy equation

$e = m {c}^{2}$

$\frac{hc}{λ} = m {c}^{2}$

$λ = \frac{h}{mv}$

$debroglie \: equation$

$λ = \frac{h}{p} = \frac{h}{ \sqrt{</strong><strong>2mK</strong><strong>.E</strong><strong>} }$

No.of waves formed by electron =orbit number n.

λ=root(150/v) in angstroms.