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An electron of mass m is moving in an electric field \(\vec{E}=-2{E}_{\mathrm{o}}\overset{^}{i}\left({\mathrm{E}}_{\math…

Q1

An electron of mass m is moving in an electric field \(\vec{E}=-2{E}_{\mathrm{o}}\overset{^}{i}\left({\mathrm{E}}_{\mathrm{o}}=\text{ constant }>0\right),\) with an initial velocity \(\vec{V}={v}_{\mathrm{o}}\overset{^}{i}\left({v}_{\mathrm{o}}=\text{ constant }>\right.\)\(0)\text{. If }{\lambda }_{\mathrm{o}}=\frac{h}{4m{v}_{\mathrm{o}}}\text{, }\) its de Broglie wavelength at time t is ________. (e = charge of electron).

[JEE Main 2026, 5 Apr (Shift 1)]

a

\(\frac{4{\lambda }_{\mathrm{o}}}{\left[1-\frac{{E}_{\mathrm{o}}e}{2m}\frac{t}{{v}_{\mathrm{o}}}\right]}\)

b

\(\frac{4{\lambda }_{\mathrm{o}}}{\left[1+\frac{{E}_{\mathrm{o}}e}{2m}\frac{t}{{v}_{\mathrm{o}}}\right]}\)

c

\(\frac{4{\lambda }_{\mathrm{o}}}{\left[1+\frac{2{E}_{\mathrm{o}}e}{m}\frac{t}{{v}_{\mathrm{o}}}\right]}\)

d

\(\frac{4{\lambda }_{\mathrm{o}}}{\left[1-\frac{2{E}_{\mathrm{o}}e}{m}\frac{t}{{v}_{\mathrm{o}}}\right]}\)

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