Question

De broglier dual nature of matter

Answer 1

a)    The whole universe is composed of matter and electromagnetic radiations. Since both are forms of energy so can be transformed into each other.

(b)   The matter loves symmetry.  As the radiation has dual nature, matter should also possess dual character.

According to the de Broglie concept of matter waves, the matter has dual nature. It means when the matter is moving it shows the wave properties (like interference, diffraction etc.) are associated with it and when it is in the state of rest then it shows particle properties. Thus the matter has dual nature. The waves associated with moving particles are matter waves or de-Broglie waves.

WAVELENGTH OF DE-BROGLIE WAVES

Consider a photon whose energy is given by

E=hυ=hc/λ            – – (1)

If a photon possesses mass (rest mass is zero), then according to the theory of relatively ,its energy is given by

E=mc2 – – (2)

From (1) and (2) ,we have

Mass of photon m= h/cλ

Therefore Momentum of photon

P=mc=hc/cλ=h/λ    – – (3)

Or           λ = h/p

If instead of a photon,  we consider a material particle of mass m moving with velocity v,then the momentum of the particle ,p=mv. Therefore, the wavelength of the wave associated with this moving particle is given by:

h/mv                                      –

Or           λ = h/p  (But here p = mv)           (4)

This wavelength is called DE-Broglie wavelength.

Special Cases:

1. dE-Broglie wavelength for material particle:

If E is the kinetic energy of the material particle of mass m moving with velocity v,then

E=1/2 mv2=1/2 m2v2=p2/2m

Or              p=√2mE

Therefore the by putting above equation in equation (4), we get de-Broglie wavelength equation for material particle as:

λ = h/√2mE     – – (5)

Answer 2

French physict DE broglie   in 1924 proposed the matter like radiation should also exhibit dual behaviour i.e both particle and wave like properties.