An electron of mass $m$ with an initial velocity $\overrightarrow v= v_0\hat i$$( v_o > 0 )$ enters in an electric field $\overrightarrow E = -E_0 \hat i$ $(E_0 = \text{constant}>0)$ at $t=0.$ If $\lambda_0,$ is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time $t?$
1. $\frac{\lambda_0}{\left(1+ \frac{eE_0}{mv_0}t\right)}$
2. $\lambda_0\left(1+ \frac{eE_0}{mv_0}t\right)$
3. $\lambda_0 t$
4. $\lambda_0$

When the light of frequency $2\nu_0$ (where $\nu_0$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is $v_1.$ When the frequency of the incident radiation is increased to $5\nu_0,$ the maximum velocity of electrons emitted from the same plate is $v_2.$ What will be the ratio of $v_1$ to $v_2?$

The photoelectric threshold wavelength of silver is $3250\times 10^{-10}~\text{m}.$ What will be the velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength $2536\times 10^{-10}~\text{m}?$ 
(Given $h= 4.14\times 10^{-15}~\text{eVs}$ and $c= 3\times 10^{8}~\text{m/s}$)
1. $\approx 0.6\times 10^{6}~\text{m/s}$
2. $\approx 61\times 10^{3}~\text{m/s}$
3. $\approx 0.3\times 10^{6}~\text{m/s}$
4. $\approx 0.3\times 10^{5}~\text{m/s}$

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)

<sup>$1.$ ${\left(\frac{E}{2m}\right)}^{1/2}$

$2.$ $c{\left(2mE\right)}^{1/2}$

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

$4.$ $\frac{1}{c}{\left(\frac{E}{2m}\right)}^{1/2}$</sup>