Question

Electrons 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

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

Answer 1

Answer: (B)

decrease by 2 times

Answer 2

$\lambda=\frac{ h }{\sqrt{2 \,mq \,\Delta V }} \propto \frac{1}{\sqrt{\Delta V }}$
$\frac{\lambda_{2}}{\lambda_{1}}=\sqrt{\frac{\Delta V _{1}}{\Delta V _{2}}}=\sqrt{\frac{25}{100}}=\frac{1}{2}$
$\lambda_{2}=\frac{\lambda_{1}}{2}$