The French physicist **Louis de Broglie** made a bold assertion in 1923. Considering Einstein's relationship of wavelength lambda to momentum p, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:

**lambda = h / p** Where ** h ** is **Planck's constant** and **p** is ** momentum**.

This wavelength is called the **de Broglie wavelength**.

According to de Broglie, an electron of mass ‘m’ moving with a velocity ‘v’ should be associated with a wave having wave length (lambda). This wave length and velocity are related by the following mathematical equation =>

…

Where h is the Planck's constant and mv is the momentum of the moving particle. Equation is known as de Broglie relationship and can be written as

or mv µ …

Equation (2) is another form of de Broglie relationship and this can be stated in words as “The momentum of a moving particle is inversely proportional to the wave-length of the waves associated with it.”

E = hn …

If we now consider it as a particle of mass m, its energy is given by

E = mc2 …

From equation (3) and (4), we get

hn = mc2 …

As the photon travels in free space with velocity of light c, its momentum p is given by

P = mass ´ velocity = mc …

On dividing equation (5) by (6), we get

or [ c = vl = Frequency ´ wave length]

or …

de-Broglie assumed that the above relation holds good for material particles like electrons, and hence for electrons eq. (7) becomes as

…

Where m is the mass, v the velocity, l the wave length and p the momentum of an electron. Equation (8) is same as equation (1).

For the wave to remain continually in phase, the circumference of the orbit should be an integral multiple of wavelength l i.e.,

2pr = nl …

Where r is the radius of the orbit and n is a whole number.

From equation (8), we get

l = h/mv …

Substituting the value of l in equation (9), we get

or …

Which is the same as Bohr's second postulate. From equation

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