Question

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

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

Answer 1

The correct option is B decrease by $2$ times

As the kinetic energy (K) of the electron is equal to the energy gained from accelerating through the electric potential (V), so

$\frac{p^2}{2m}=eV....\left(1\right)$

The de-Broglie wavelength, $\lambda =h/p$

Now (1) becomes, $\frac{h^2}{2m{\lambda }^2}=eV$

so , $\lambda \propto \frac{1}{\sqrt{V}}$

Thus, $\frac{{\lambda }_2}{{\lambda }_1}=\sqrt{\frac{V_1}{V_2}}=\sqrt{25/100}=1/2$