Question

what do you mean by dual nature of matter ? show that de- Broglie's wave length is inversely proportional to the velocity of the particle

Answer 1

In case of light some phenomenon like diffraction and interference can be explained on the basis of its wave character. ... Louis de Broglie, in 1924 extended the idea of photons to material particles such as electron and he proposed that matter also has a dualcharacter-as wave and as particle.

Answer 2

Answer :

As we know that matter has dual nature that is particle nature as well as wave nature.

Particle nature means that the light always travel in a straight line. Particle nature is observed through the photoelectric effect.

Wave nature is illustrated through experiment on the diffraction and interference.

According to the De-Broglie's wave, every fast moving matter particle is associated with a wavelength known as De-Broglie's wavelength. He cosidered both the nature that is, particle nature and wave nature.

As per particle nature,

$E=mc^2$      .........(1)

As per wave nature,

$E=h\nu$       ..........(2)

From equation 1 and 2, we get

$mc^2=h\nu\\\\mc^2=h\frac{c}{\lambda}\\\\\lambda=\frac{h}{mc}$

But non of the particle has got velocity equal to speed of light.

Therefore, v < c

The formula will be,

$\lambda=\frac{h}{mv}$

From this we conclude that the wavelength is inversely proportional to the velocity of the light.