**THE DUAL BEHAVIOUR OF MATTER**

Einstein had suggested in 1905 that light has dual nature, that is, wave nature as well as particle nature. In 1923, Louis de-Broglie , the French physicist proposed that like light, matter also has dual character. It exhibits wave as well as particle nature. He even derived a relationship for the calculation of wavelength (A) of the wave associated with a particle of mass m, moving with velocity v as given below:

λ =h / mv or λ =h/p

where h is Planck’s constant and p is momentum of the particle.

The waves associated with material particles or objects in motion are called matter waves or de-Broglie waves. These waves are distinctively different from the electromagnetic waves.

The wave nature of electrons was experimentally verified by Davisson and Germer by electron diffraction experiment.

**SIGNIFICANCE OF de-BROGLIE WAVES**

The wave character puts some restriction on how precisely we can express the position of an electron or any other small moving particle. This is due to the reason that unlike particles, waves do not occupy a well defined position in space and are delocalised. The wave nature of matter, however, has no significance for objects of ordinary size because wavelength of the wave associated with them is too small to be detected.** **

**SOLVED EXAMPLES**

**Example 5.8** Calculate the wavelength of a body of mass 1 mg moving with a velocity of 10 m sec^{-1}.** **

**Solution. **We know, A =λ /mu

Substituting the values, m = 1 mg = 10^{-6} kg,

and u =10 m sec-1

h =6.626 x 10^{-34} kg m2 s-1

λ =6.626 x 10^{-34} kg m2 s-1 / 10^{-6} kg x 10ms-1

= 6.626 x 10^{-29} m.

**Example 5.9** Calculate the wavelength of an electron moving with a velocity of 2.05 x 10^{7} m r1.

**Solution . **λ = h mu

= 6.626 x10^{-34} kg m^{2} s-1 / 9.1 x 10^{-31} kg x 2.05 x 10^{7} ms^{-1}

= 3.55 x10^{-11} m.