Question

What possibly can be the ratio of the de Broglie wavelength of two electrons having the same initial energy and accelerated through $50\text{V}$ and $200\text{V}$

• A. $3:5$
• B. $10:3$
• C. $6:2$
• D. $2:1$

Answer 1

The correct option is D $2:1$

We know that,
de broglie wavelength, $\lambda =\frac{1}{\sqrt{2meV}}$
Where, $V=\text{potential}$
$m=\text{mass of electron}$
So, $\lambda \propto \frac{1}{\sqrt{V}}$
Given that electrons are accelerated through $50\text{V}$ and $200\text{V}$ respectively, therefore,
$\frac{{\lambda }_1}{{\lambda }_2}=\frac{\sqrt{V_2}}{\sqrt{V_1}}=\frac{\sqrt{200}}{\sqrt{50}}=2:1$