Question

What possibly can the ratio be of the de Broglie wavelengths for two electrons having the same initial energy and accelerated through 50 volts and 200 volts?

• A. 3 : 10
• B. 10 : 3
• C. 1 : 2
• D. 2 : 1

Answer 1

The correct option is D 2 : 1

The De-Broglie equation is $\lambda =\frac{h}{mv}$. .....(1)

The expression for the kinetic energy of electron when it accelerated through a potential of V volts is $E=\frac{1}{2}m{u}^2=eV$.

Rearrange above equation
$u=\sqrt{\frac{2eV}{m}}$. .....(2)

Substitute equation (2) in equation (1)

$\lambda =\frac{h}{m\sqrt{\frac{2eV}{m}}}$

Two electrons are accelerated through 50 volts and 200 volts.

$\frac{\lambda }{{\lambda }^{\prime }}=\sqrt{\frac{V^{\prime }}{V}}=\sqrt{\frac{200}{50}}=2$

Hence, the ratio of the de Broglie wavelengths for two electrons is 2:1.

Hence, the correct option is $D$