Question

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

• A. increase by $2$ times
• B. decrease by $2$ times
• C. increase by $4$ times
• D. decrease by $4$ times

Answer 1

The correct option is B decrease by $2$ times

de_broglie wavelength $\lambda =\frac{h}{P}$
where momentum of the particle $P=\sqrt{2mK}=\sqrt{2meV}$
$⟹\lambda =\frac{h}{\sqrt{2meV}}$
We get $\lambda \propto \frac{1}{\sqrt{V}}$
Given : $V_i=25kV$ and $V_2=100kV$
So, voltage is increased by a factor of $4$.
Thus wavelength gets reduced by a factor of $2$.