What is de Broglie equation and how to explain it

de Broglie gave the concept of dual nature of matter. Matter has particle nature as well as wave nature. Here, we will study the Broglie equation and its relationship.

de Broglie concept of dual nature

  1. Like light, matter has also dual nature. ( particle nature and wave nature )
  2. The equation that relates the dual nature: wavelength = h/mv = h/p where m is the mass, v = velocity and p = momentum of material particle.
  3. It is applicable to all material particles. But it is significant for microscopic particles only.
  4. Davisson and Germer verified the wave character of material particle.
  5. Scintillation experiment proved the particle nature.

Significance of de Broglie equation

It is applicable to all material particles. But it is significant for microscopic particles only. Let’s understand this concept with an example.

Consider a ball of mass 0.1 kg moving with a speed of 60 m/s. Applying Broglie equation, wavelength = h/mv = 10 ^-34m. The associated wavelength is so small to observe.

On the other hand, an electron with a rest mass of 9.1 X 10^-31 Kg has the associated wavelength = 10^5 A degree. This wavelength is easy to observe.

Since, we mainly come across macroscopic objects in everyday life. Therefore, Broglie relationship has no significance in daily life.

Experimental verification of dual nature of electrons

A) Verification of wave nature

  1. Davisson and Germer performed an experiment in 1927
  2. They passed a beam of electrons on the surface of Ni crystal.
  3. And they observed the reflected rays received on a photographic plate.
  4. There was a diffraction pattern similar to that of X-rays.
  5. X-rays are electromagnetic waves. They have wave character and so that of an electron.
  6. The wavelength determined from the Diffraction pattern is same as calculated from d Broglie eq.

B) Verification of Particle nature

The particle nature of the electron is proved by the scintillation method.

  1. When an electron strikes a ZnS screen, a spot of light is produced. This is called as scintillation.
  2. Since scintillation is localised on ZnS screen, so the striking electron must be localised.
  3. But particles has localised character, so that of the electron.

Check out the Electromagnetic wave theory here

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