Name: de-Broglie Hypothesis
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: There is a longstanding debate as to whether light is a wave or a particle. It is not limited to light. What about humans? Let us explore the logic of De Bro...

Question

Mention de-Broglie hypothesis and describe in detail the experiment of Davisson and Germer for its experimental verification.

Accepted Answer

De-Broglie put forward a hypothesis that as light energy exhibits dual nature, matter should also show dual nature, i.e. in some circumstances matter should behave like waves. He suggested that the formula, $λ = \frac{h}{p}$ for photon should also be applicable on a particle.

Davisson and Germer thought if particles like electron have wave property then they should also be diffracted by the crystal like x-rays.

The experimental set up of Davisson and Germer experiment is as shown below:

A beam of high energy electrons is obtained from an electron gun which is further accelerated using diaphragms kept at high positive potential. The electron beam is incident on the Nickel crystal normally and the scattered electrons are collected in a detector. By moving the detector in a circular path the angle between incident electron beam and scattered beam can be changed.

By analysing the intensity of diffracted beam and angle of diffraction from various values of accelerating voltage it is evident that when the accelerating voltage is $54 V$ , the intensity in the detector is maximum at $50 °$ .

Using Bragg's law $(d \sin θ = n λ)$ , the wavelength can be determined. Hence, for $d = 2.15 Å$ , $θ = 50 °$ and $n = 1$ as it is for first order diffraction, we get the wavelength to be,

$λ = 2.15 \times \sin 50 ° = 2.15 \times 0.766 = 1.65 Å$ .

According to de-Broglie, the wavelength of matter wave at $V = 54 V$ is

$λ = \frac{12.27 Å}{\sqrt{V}} = \frac{12.27 Å}{\sqrt{54}} = 1.67 Å$ .

Thus, the experimental value of wavelengths from Davisson and Germer experiment is very close to de-Broglie wavelength. This concluded that diffraction of electron beam is possible and thus verified matter waves as in the hypothesis of de-Broglie.

Mention de-Broglie hypothesis and describe in detail the experiment of Davisson and Germer for its experimental verification.

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