Electrons used in an electron microscope are accelerated by a voltage of $25 \mathrm{kV}$. If the voltage is…
Electrons used in an electron microscope are accelerated by a voltage of $25 \mathrm{kV}$. If the voltage is increased to $100 \mathrm{kV}$ then the de-Broglie wavelength associated with the electrons would
decrease by 2 times
decrease by 4 times
increase by 4 times
increase by 2 times
Solution
We have
$\lambda=\frac{12.27}{\sqrt{V}}$
$\mathrm{SO}$,
$\begin{aligned}
& \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{V_1}} \\
& \lambda_2=\lambda_1 \sqrt{\frac{V_1}{V_2}} \\
& \lambda_2=\lambda_1 \sqrt{\frac{25}{100}} \\
& \lambda_2=\lambda_1 \sqrt{\frac{1}{4}}=\frac{\lambda_1}{2}
\end{aligned}$