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