De Broglie Wavelength Formula

Louis-de-Broglie explained the De-Broglie waves in the year 1923 which were later experimented and proved by Davisson and Germer in the year 1927. These waves explain about the nature of the wave related with the particle.

Einstein explained  the momentum (p) of a photon with the given formula

The energy (E) of a photon regarding wavelength is given by

Where h = Planck’s constant.

The formula explains the momentum of the photon (p)

Where,

h= planck’s constant,

c = velocity of light.

Hence, the De-broglie wavelength (λλ) is given by

De Broglie Wavelength Formula is used to calculate the wavelength and momentum in any given problems based on this concept.

Question 1: Find the wavelength of an electron moving with a speed of 2 ×× 106 ms-1.

Solution:

Given:

Velocity of electron, v = 2 ×× 106 ms-1,

Mass of electron, m = 9.1 ×× 10-31 Kg

Planck’s Constant, h = 6.623 ×× 10-34 Js,

The de-broglie wavelength is given by λλ = hmvhmv

                                                                      = 6.623×10−349.1×10−31×2×1066.623×10−349.1×10−31×2×106

                                                                      = 3.63 ×× 10-10 m

                                                                      = 3.63 A0

Question 2: Find the de-broglie wavelength of the stone of mass 0.1 Kg moving at a speed of 5 ms-1.

Solution:

Given: Planck’s Constant h = 6.63 ×× 10-34 Js,

Mass of the stone m = 5 ms-1,

Velocity of stone v = 0.01 Kg,

De-broglie wavelength λλ = hmvhmv

                                                = 6.23×10−345×0.016.23×10−345×0.01

                                                = 1.32 ×× 10-32 m.

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