Question

Electrons used in an electron microscope are accelerated through a voltage of $25\text{kV}$. If voltage is increased to $100\text{kV}$ then the de-Broglie wavelength associated with the electrons will

• A. increased by $4$ times.
• B. be doubled.
• C. be halved.
• D. decreased by $4$ times.

Answer 1

The correct option is C be halved.

From $\lambda =\frac{h}{\sqrt{2m\left(qV\right)}}$

$\Rightarrow \lambda \propto \frac{1}{\sqrt{V}}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{\sqrt{V_2}}{\sqrt{V_1}}=\frac{\sqrt{100}}{\sqrt{25}}=2$

$\Rightarrow {\lambda }_2=\frac{{\lambda }_1}{2}$
So, it will be halved.
Hence, $\left(C\right)$ is the correct answer.