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An electron of mass ' m ' with an initial velocity \(\vec{v}={v}_{0}\overset{^}{i}\left({v}_{0}>0\right)\) enters an ele…

Q1

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

[JEE Main 2025, 24 Jan (Shift 1)]

a

\(\frac{{\lambda }_{0}}{\sqrt{1-\frac{{e}^{2}{E}_{0}{{}^{2}t}^{2}}{{m}^{2}{{v}_{0}}^{2}}}}\)

b

\(\frac{{\lambda }_{0}}{\sqrt{1+\frac{{e}^{2}{E}_{0}{{}^{2}t}^{2}}{{m}^{2}{{v}_{0}}^{2}}}}\)

c

\({\lambda }_{0}\)

d

\({\lambda }_{o}\sqrt{1+\frac{{e}^{2}{E}_{0}^{2}{t}^{2}}{{m}^{2}{v}_{o}^{2}}}\)

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