# Electron 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 Option 1) increase by 2 times Option 2) decrease by 2 times Option 3) increase by 4 times Option 4) increase by 4 times

S subam

As we discussed in concept

De - Broglie wavelength with charged particle -

$\lambda = \frac{h}{\sqrt{2mE}}= \frac{h}{\sqrt{2mE}}$

$\lambda = \frac{h}{\sqrt{2mqv}}$

- wherein

$E\rightarrow kinetic\: energy\: o\! f particle$

$q\rightarrow charged \: particle$

$\lambda\:=\: \frac{h}{\sqrt{2mev}}\:=>\: \lambda\propto \frac{1}{\sqrt{V}}$

$\therefore \frac{\lambda_{2}}{\lambda_{1}}\:=\: \sqrt{\frac{V_{1}}{V_{2}}}\:=\:\sqrt{\frac{1}{4}}\:=\:\frac{1}{2}$

$\therefore$ wavelength decreases by a factor of 2.

Option 1)

increase by 2 times

This option incorrect.

Option 2)

decrease by 2 times

This option correct.

Option 3)

increase by 4 times

This option incorrect.

Option 4)

increase by 4 times

This option incorrect.

Exams
Articles
Questions