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Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would

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increase by 2 times

decrease by 2 times

decrease by 4 times

increase by 4 times

answer is B.

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Detailed Solution

de Broglie wavelength of an electron accelerated through potential difference V,

$λ = \frac{h}{p} = \frac{h}{\sqrt{2 mE}} = \frac{h}{\sqrt{2 meV}}$

$∴ λ \propto \frac{1}{\sqrt{V}}$

$\Rightarrow \frac{λ_{2}}{λ_{1}} = \sqrt{\frac{V_{1}}{V_{2}}} = \sqrt{\frac{25}{100}} = \frac{1}{2}$

$\Rightarrow λ_{2} = \frac{λ_{1}}{2}$

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