Explanation of the concept of de-Broglie equation or Dual Nature of Particles.
De Broglie’s Equation or the Concept of Dual Nature of Particles:
In 1924, de Broglie proposed an equation to explain the particle and wave nature of electrons by combining Max Planck’s quantum equation of radiation and Einstein’s mass-energy equation, which is widely known as de Broglie’s equation.
Max Planck’s quantum equation regarding radiation is—
Again, Einstein’s equation regarding energy is—
From equations (i) and (ii), we get,
or, mc2 = h ·
or, mc =
or, λ · mc = h
or, λ =
or, λ =
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De Broglie’s equation is not only applicable to photons but also to all moving objects. To apply it to any general object, the velocity of light c must be replaced by the velocity of the object v. In this case—
or, λ =
Bohr’s Theory and the Wave Nature of Electrons:
According to de Broglie, an electron behaves like a standing wave in a circular orbit around the atomic nucleus. To complete a stable wave-train around the circumference of the orbit, the circumference must be an integral multiple of the wavelength. In other words—
or, 2πr = n ·
or, 2πr · mv = nh
or, mvr =
This equation shows that the angular momentum of an electron in Bohr’s model is an integral multiple of $h/2\pi$, which is a key postulate of Bohr’s theory. Therefore, Bohr’s equation for angular momentum can easily be derived from de Broglie’s equation.
