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Deduce the de-Broglies matter wave equation.

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Dual nature of electron – de Broglie's matter-wave equation 

According to Einstein’s mass-energy relation, E = mc2 … (1) 

Where m and c are the mass and velocity of an electron respectively. 

According to quantum theory, Energy E = hv = (he) / λ … (2) 

Where h is Plank’s constant = 6.626 × 10-34 Js, u is the frequency of moving electron. 

Comparing(1) and (2) me2 = (hc)/λ >me = h/λ > = λ = h /me … (3) 

Equation (3) is called de-Broglie’s equation. 

For an electron its velocity is given as V, So the de-Broglie’s equation for an electron is given by, 

λ = h / mv (mv = p = momentum of electron) 

λ = h / p is called de-Broglie’s matter – wave equation

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