Mention the significance of Davisson and Germer’s experiment. An α-particle and a proton are accelerated from rest through the same potential difference V. Find the ratio of de-Broglie wavelengths associated with them.

Solution

The Davisson and Germer’s experiment established famous de-Broglie hypothesis of wave-particle duality by confirming the wave nature of moving particle.

Given, an alpha particle and a proton are accelerated from rest by the same potential.

The energy acquired by alpha-particle, E_α = 2eV
The energy acquired by proton, E_p = eV

$de - Broglie wavelength, λ = \frac{h}{\sqrt{2 mE}}$

Hence, the ratio of wavelengths,

$\frac{λ_{α}}{λ_{p}} = \frac{\sqrt{m_{p} E_{p}}}{\sqrt{m_{α} E_{α}}} = \frac{\sqrt{m_{p} E_{p}}}{\sqrt{(4 m_{p}) (2 E_{p})}} [∵ m_{α} = 4 m_{p} and E_{α} = 2 E_{p}]$

$\Rightarrow$ $\frac{λ_{α}}{λ_{p}} = \frac{1}{2 \sqrt{2}}$

i.e., $λ_{α} : λ_{p} = 1 : 2 \sqrt{2} .$

is the obtained ratio of the de-broglie wavelength asosciated with the particles.

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Wave Optics

Mention the significance of Davisson and Germer’s experiment. An α-particle and a proton are accelerated from rest through the same potential difference V. Find the ratio of de-Broglie wavelengths associated with them.

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