A stream of electrons from a heat filament was passed between two charge 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

Question

A stream of electrons from a heat filament was passed between two charge 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 the electron wave) is given by:

TestHub · Accepted Answer

Given, stream of electron from heated filament was passed between two charge plates at potential difference $V$ .
$e and m$ are charge and mass of electron, respectively.
$V = \frac{Energy}{e}$
$e V = \frac{1}{2} \times m \times v^{2}$
$λ = \frac{h}{m v} v = \frac{h}{m λ}$
$e V = \frac{1}{2} \times m \times {[\frac{h}{m λ}]}^{2}$
$\frac{h}{λ} = \sqrt{2 m e V}$

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