An electron of mass \(m\) with an initial velocity \(\overrightarrow v= v_0\hat i\)$\stackrel{}{}$\( ( v_o > 0 ) \) enters in an electric field \(\overrightarrow E = -E_0 \hat i\) \((E_0 = \text{constant}>0)\) at \(t=0.\) If \(\lambda_0,\)${\mathrm{}}_{}$ is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time \(t?\)

An electron of mass m and a photon have the same energy E. Find the ratio of de-Broglie wavelength associated with the electron to that associated with the photon. (c is the velocity of light)

^{$1.$ ${\left(\frac{E}{2m}\right)}^{1/2}$
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$2.$ $c{\left(2mE\right)}^{1/2}$
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$3.$ $\frac{1}{c}{\left(\frac{2m}{E}\right)}^{1/2}$
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$4.$ $\frac{1}{c}{\left(\frac{E}{2m}\right)}^{1/2}$}