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Question

The wave nature of particles was studied using diffraction of particle beams by crystal lattices. The wavelength of the waves associated with fast moving particles was found to be in agreement with the de Broglie relation.
For a particle of mass m moving with kinetic energy E, the de Broglie wavelength is

A
h2mE
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B
h2mE
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C
h2mE
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D
h2mE
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Solution

The correct option is D h2mE
The energy of photon is
E=hν
According to Einstein's energy mass relation
E=mc2
From above equations
hν=mc2

hcλ=pc ..................(since, p=mc)

λ=hp

This is the De-Broglie's equation for wavelength for the photon.
For the particle having mass m and velocity v, De-Broglie's equation for wavelength becomes

λ=hmv .................(1)

The energy of the particle is

E=12mv2

E=p22m

p=2mE
using this value in (1), we get

λ=h2mE

So, the answer is an option (C).

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