Modern Physics | JEE Main Solution | de Broglie Wavelength

JEE MAIN 2025

24-01-2025 SHIFT-1

Question

An electron of mass 'm' with an initial velocity $\overrightarrow {\rm{v}} = {{\rm{v}}_0}\hat i\left( {{{\rm{v}}_0} > 0} \right)$ enters an electric field $\overrightarrow {\rm{E}} = - {{\rm{E}}_{\rm{O}}}\widehat {\rm{k}}$ . If the initial de Broglie wavelength is ${\lambda _0}$, the value after time t would be Options

Select the correct option:

$\frac{{{\lambda _0}}}{{\sqrt {1 - \frac{{{{\rm{e}}^2}{\rm{E}}_0^2{{\rm{t}}^2}}}{{\;{{\rm{m}}^2}{\rm{v}}_{\rm{o}}^2}}} }}$

${\lambda _0}$

${\lambda _{\rm{o}}}\sqrt {1 + \frac{{{{\rm{e}}^2}{\rm{E}}_{\rm{o}}^2{{\rm{t}}^2}}}{{\;{{\rm{m}}^2}{\rm{v}}_{\rm{o}}^2}}} $

$\frac{{{\lambda _o}}}{{\sqrt {1 + \frac{{{{\rm{e}}^2}E_o^2{{\rm{t}}^2}}}{{{m^2}v_o^2}}} }}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution