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 moving with kinetic energy , the de Broglie wavelength is

A

B

C

D

Hard

Solution

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Correct option is C)

The energy of photon is

According to Einstein's energy mass relation

From above equations

..................(since, )


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 

.................(1)

The energy of the particle is




using this value in (1), we get

 

So, the answer is an option (C).

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