Monochromatic light of frequency $6 \times 10^{14} \mathrm{~Hz}$ is produced by a laser. The power emitted is $2 \times 10^{-3} \mathrm{~W}$.

How many photons per second on an average, are emitted by the source ?

(Given $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ )

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than $660 \mathrm{~nm}$. The band gap of photodiode is found to be $\left(\frac{\mathrm{X}}{8}\right) \mathrm{eV}$. The value of $\mathrm{X}$ is :

(Given, $\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ )

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2 \lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :