**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 = mc

^{2}
Here 'c' is velocity of light.

Energy of photon E = hv

∴ hv = mc^{2}

But, v = c / λ

∴ hc / λ = mc

^{2}

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 (A

^{o})

Wave length of Helium atom 0.71 (A

^{o})

Wave length of Xenon atom 0.12 (A

^{o})

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