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### De-Broglie hypothesis and De-Broglie equation

De-Broglie Hypothesis

In 1924, de-Broglie proposed that matter has a dual character, as wave and as particle.

In Bohr theory, electron is treated as particle. But according to De-Broglie, electron has a dual dual character; both as a material particle and as a wave. He derived an expression for calculating the wave length 'λ' of a particle of mass 'm'  moving with velocity 'v'.

According to this,
wave length = λ =  h / mv  , where 'h' is Planck's constant

This is equation is known as De-Broglie's equation and it is an expression for wave - matter dualism.

The waves associated with particles in motion are called matter waves or De-Broglie waves. They differ from electromagnetic radiations. They have lower velocities, and no electrical and magnetical fields associated with them.

Derivation of  De-Broglie's equation

The de-Broglie's equation can be derived by using the mass energy relationship suggested by Einstein.

E = mc2
Here 'c' is velocity of light.

Energy of photon  E = hv

∴   hv = mc2

But, v = c /  λ

∴  hc / λ  =  mc2

h / λ  = mc

Hence  λ  =  h / mc

Repalcing 'c' by velocity of a particle 'v'.

λ  =  h / mv

Since  mv  = p (momentum)

λ  =  h / p

de-Broglie's wave length of certain particles at 25 o C

Wave length of Electron  60.67 (Ao)
Wave length of Helium atom  0.71 (Ao)
Wave length of Xenon atom  0.12  (Ao)