Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV has a de-Broglie wavelength of λ 0 . If the voltage is increased to 40 kV then the de-Broglie wavelength associated

Question

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV has a de-Broglie wavelength of λ 0 . If the voltage is increased to 40 kV then the de-Broglie wavelength associated with the electron beam would be:

TestHub · Accepted Answer

The de-Broglie wavelength of an electron accelerated through potential $V$ is

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m (KE)}} = \frac{h}{\sqrt{2 meV}}$

where, $h$ is Planck's constant, $e$ is charge of electron and $m$ is mass of electron.

From above relation, $λ \propto \frac{1}{\sqrt{V}}$

$∴ \frac{λ}{λ_{0}} = \sqrt{\frac{20}{40}}$

$\Rightarrow λ = \frac{λ_{0}}{\sqrt{2}}$ .

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