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 = mc2But, 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)
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