An electron of mass $m$ is moving in an electric field $\vec{E}=-2 E_{\mathrm{o}} \hat{i}\left(E_{\mathrm{o}}=\right.$ constant $\left.>0\right)$, with an initial velocity $\vec{V}=v_{\mathrm{o}} \hat{i} \left(v_{\mathrm{o}}=\right.$ constant $\left.>0\right)$. If $\lambda_{\mathrm{o}}=\frac{h}{4 m v_{\mathrm{o}}}$, its de Broglie wavelength at time $t$ is

$\_\_\_\_$ .

( $e=$ charge of electron)

In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit $(f)$. The ratio of the radius of the orbits in given by $r_i: r_f=16: 4$. The wavelength of photon emitted due to this transition is $\_\_\_\_$ nm.

(Given Rydberg constant $=1.0973 \times 10^7 / \mathrm{m}$ )

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6 \mu \mathrm{~F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^6 \mathrm{~V} / \mathrm{s}$. The value of $\alpha$ is $\_\_\_\_$ .

Refer to the figure given below, current between terminals $A$ and $B$ is