Deduce the de-Broglies matter wave equation.

1.	Deduce the de-Broglies matter wave equation.
Answer» 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

Answer»

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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