Particle and wave duality, de-Broglie Relation

Particle and wave duality

In 1905, Einstein had suggested that light has duel character. In analogy with the behaviour of light, de Broglie suggested that all material particles should also show dual behaviour. In 1924, de Broglie suggested that electron has duel character. This suggestion recieved first experimental support from Davission and German in 1927. They found that the impact of electron on crystal resulted in the production of diffraction pattern which were similar to those given by x-rays under similar condition. Since x-rays posses wave character, electrons must also have wave character associated with them. Thus this experiment gave direct evidence for wave character of electrons, nutrons, protons, hydrogen atom, C60 (fullerene) etc.

The similarity of these two patterns shows that electrons can behave like X-rays and display wave properties.

de-Broglie Relation

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

In Bohr theory, electron is treated as a particle. But according to de-Broglie, electron has a duel character; both as a material particle and 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,

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

The wave 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 magnetic fields associated with them.

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

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

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