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A stream of electrons from a heated filaments was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/λ (where λ is wavelength associated with electron wave) is given by:

1. √meV
2. √2meV
3. meV
4. 2meV

Correct answer: √2meV

Solution

The de Broglie wavelength of an electron is related to its momentum, which is influenced by its kinetic energy. When an electron is accelerated through a potential difference V, it gains kinetic energy equal to eV, and using the relationship between kinetic energy and momentum, we find that the wavelength is inversely proportional to the square root of the mass and the potential difference, leading to the result of √2meV for h/λ.

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