De-Broglie’s Relation

According to De Broglie, every particle in motion has wave character. Even we possess wave character. The wave associated with matter is called matter wave. The wavelength associated with the the matter is given by:

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

$$\text{According to Einstein’s Law,}$$

$$E =  mc^2……(i)$$

$$\text{According to Planck’s law,}$$

$$E =  hf……(ii)$$

$${From equation (i) and (ii),}$$

$$mc^2 = h\lambda $$

$$or, mc^2 = \frac{hc}{\lambda}$$

$$or, \lambda = \frac{h}{mc}$$

$$\text{So, for a matter}$$

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

$$\therefore \lambda = \frac{h}{p}……(iii)$$

Equation (iii) is the mathematical expression for De Broglie’s relation.

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