Find the de Broglie wavelengths for both an electron and a proton moving at a sp

Question

Find the de Broglie wavelengths for both an electron and a proton moving at a speed of 7.80 times 10^5 m/s. Electron lambda = nm Proton lambda = nm Comment on whether either of these wavelengths could be detected by diffraction effects in crystals. Both the electron and the proton wavelengths are too short to be detected by crystals. The proton wavelength is comparable to atom spacing in a crystal but the electron wavelength is too long. Both the electron and the proton wavelengths can be detected by crystals. The proton wavelength is comparable to atom spacing in a crystal but the electron wavelength is too short. The electron wavelength is comparable to atom spacing in a crystal but the proton wavelength is too short.

Explanation / Answer

De-Broglie wavelength of a particle is given by =h/mv

where, h is planck's constant

m is the mass of the particle

v is the velocity of the particle

For an electron m= 9.1 x 10-31 Kg

For a proton, m = 1.67 x 10-27 Kg

Velocity of the particle, v = 7.8 x 105 m/s

Planck's constant, h = 6.626 x 10-34  J-s

So, de-Broglie wavelength of an electron is given by

=h/mv = 6.626 x 10-34 /9.1 x 10-31 x7.8 x 105 = 9.34 x 10-10 m

So, de-Broglie wavelength of a proton is given by

=h/mv = 6.626 x 10-34 /1.67 x 10-27 x7.8 x 105 = 5.09 x 10-13m

Since crystals can diffraction radiations of the order of 1A.U., we can produce

electron diffraction easily with crystals.

In the present case, both electrons and protons can be diffracted using crystals.

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