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Question:

A stream of electrons from a heated filament 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:

√meV

√2meV

2meV

meV

Solution:

Kinetic energy = eV = 1/2mu²
u = √(2eV/m). (1)
Here, u is the velocity of the electron.
The de Broglie wavelength is λ = h/mu.
h/λ = mu. (2)
Substitute equation (1) in equation (2)
h/λ = m√(2eV/m) = √(2meV)
Hence, the correct option is √2meV