**Louis de Broglie’s Hypothesis**: (Dual nature of radiations)

There arose a conflict about the nature of radiations.

There were two schools of thoughts:

** (i) wave nature and (ii) particle nature of radiations**

Both have evidences. So it is difficult to reject any.

Louis de Broglie (in 1924) solved this problem by giving the idea of dual nature of radiations through his hypothesis. It states:

“A wave is associated with sub-atomic particles, whose wavelength is inversely proportional to the momentum of the particle”

This relation shows that sub-atomic particles are wave as the have wavelength and particle as they have momentum.

Further more wavelength and momentum of the particle are inversely proportional. The lighter particles have longer wavelength while massive particles have shorter wavelength.

de Broglie’s equation was experimentally verified by two American scientists, Davison and Germer in 1927.

__Applications__:

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__Applications__De Broglie’s hypothesis is good enough to explain Bohr’s postulates.

- Bohr’s theory states that electron revolves only in orbits of particular radii and in an orbit electron does not emit or absorb energy. It is only possible when electron wave is standing wave and a wave could be standing wave if circumference of the orbit is some integral multiple of the wave length of the electron wave.

n λ = 2 π r

Circumference of orbit = 2 π r

So according to Bohr, orbits of such radius are possible only when their circumferences are some integral multiple of the electron wave. If this is so then crest of the last wave will meet crest of the first wave or trough of the last wave will meet trough of the first wave and wave will be standing wave and as a result no energy will be transmitted.

- De Broglie’s hypothesis also verifies Bohr’s postulate about angular momentum.

Apllying equation n λ = 2 π r

and putting vaue λ from de Broglie’s equation

And this is same as Bohr’s postulate about angular momentum.